OK, you get to take additional actions, that's like having a Leo De Luca in play for a few turns with some restrictions. But actually, since you get to take that additional action during any player window, not just on your own turn, you can do some more unusual things even outside of the investigation phase. There may be some shenanigans you can pull during the Mythos phase or the Upkeep phase, but the most likely target is in the player window in the Enemy phase after Hunter enemies move and engage but before any enemy attacks. You can do a basic fight to finish off a 1 HP enemy, or evade one to prevent it from dealing you any damage or horror. Or -- since playing an event is a basic action, as long as it doesn't have a Bold action modifier on it -- you can play an event card. If you don't mind or can avoid the AoO, or if the enemy isn't going to be engaging you, then you have some great options, like Call for Backup, Sneak Attack (2), and Small Favor. Coup de Grâce, Dynamite Blast (2), Blood-Rite, Manipulate Destiny, Gaze of Ouraxsh don't provoke an AoO, and may be used for different situations.

How about using that during your basic action? Most full-time Mystics will likely use this additional action for an evasion in a pinch, since they likely have a spell or two to do damage or investigate and get additional benefits. A basic evade is probably the most common way investigators with high evade anyhow, so it's not surprising this would be most likely choice for Close the Circle. But "activate" is also a basic action, so you can use this on tests on scenario cards that are otherwise difficult. Yes, most treachery cards have tests on them already, like Dreams of R'lyeh, but Locked Door is common enough. A few of the more recent campaigns have a good chunk of treachery cards at your location or in your threat area that don't give you a option, so be on the lookout if you're trying to leverage your Close the Circle.

This is by far the most interesting of the new Synergy cards. There are a number of ways you could view this card:

• A source of extra actions. At a cost of 2 resources, a play action, and the card itself, you need to get all five charges to unambiguously have a net positive (in terms of "click economy"), but if you have extra resources or actions anyway -- unlikely but possible for most mystics -- this card can be a solid way to do more things over time. It also lets you bank actions for the future.
• A source of actions. With multiple investigators, it's not uncommon to find situations where you want gator A to do some things before gator B, and some things afterward. This gives you a chance to have your cake and eat it too by letting you interleave some of their actions. The actions from this card don't provoke attacks of opportunity either, so you could also use it to, for example, move off a location that makes it harder to fight monsters before laying into them. EDIT: My understanding of the rules was incorrect. Since you are instructed to "Take" the action, the action you take will provoke AoOs. Compare e.g. Ursula's ability.
• A way to substitute for other attributes. Mystics generally like pumping their willpower anyway, so getting a chance to substitute it is always a good thing. It reminds me the most of Sword Cane in that regard; it's a handy way to evade with , or fight a 1-health monster. You could also use it to investigate, though this forfeits the action compression of spells like Rite of Seeking and secondary effects of spells like Sixth Sense. It's a good way to save a charge if there's only one clue left, or if you really don't want to worry about drawing a symbol token.

When you consider that you'll often get several of these benefits simultaneously, this card seems really potent. So what are the downsides?

• Obviously, this card requires you to run cards from several different classes (ideally, all of them) in your deck, unless you plan to manipulate charges some other way. Furthermore...
• You need to not only have multiclass cards in your deck, you need to have them on the field. This means that (1) skills and (most) events don't count, so you need to run assets, which might start to tax your slots, and (2) the order you play your cards matters a lot. If you draw this before drawing any of your multiclass cards, it's likely to just take up space in your hand for much of the game.
• It takes up an Arcane slot. This is a really big ask, since most mystics want to fill their arcane slots with some combination of an investigate spell and a fight/evade spell. Fortunately, there are many options for getting more slots, but I don't think I'd ever consider running this card without at least one of them.
• It's not a Spell. This is a surprisingly big deal, because it means it lacks synergy with most of the mystic suite. You can't reduce its cost with Robes of Endless Night or Shining Trapezohedron, and at 2 resources it's an inefficient use of Uncage the Soul. Most recharge options don't work on it (there are a few, like the newly-released Winds of Power, or Eldritch Sophist if you have access). It also can't be tutored by Arcane Initiate.
• You can only take basic actions with it. The EOTE expansion contains an FAQ (not on arkhamdb yet, to my knowledge) which defines basic actions to be those without a bold action designator on a card. So you can't use this to trigger e.g. Rite of Seeking, but you could use it for a normal investigation. This is only a minor downside in my opinion, since you take dozens of basic actions per game, so you'll have plenty of opportunities to use this.

In summary, this card has the potential to be quite useful in the right circumstances, but requires a fair bit of support (multiclass cards and extra arcane slots) to see the full effect. It's certainly worth a look for anyone who's planning to run multiclass decks anyway -- in fact, it might even be better for off-class mystics, since their arcane slots are usually less contested.

There's one mystic who really loves this card, though, and that's Akachi Onyele. She already had access to strong out-of-class cards even before Edge of the Earth dropped and she works great with "bling archmage" builds (The Hierophant • V plus Relic Hunter plus Sign Magick) which take care of the slot problems. Most importantly, though, is the fact that this card uses charges. As a result, not only does she get an additional charge each time she plays it (essentially refunding the play action), she can keep playing it over and over with her signature. Not only does this mean she can just keep getting extra actions than usual, but she can play it early (before her multiclass cards are out) without mourning the lost charges. Other mystics might be a bit skeptical, but I'm probably always going to consider this card when building an Akachi deck in the future.