Many Minds Move as One says "when *you* Gather or Push Beasts" - is that identical to "when *your actions* Gather or Push Beasts"?
Many Minds Move as One says "when you Gather or Push Beasts" - is that identical to "when your actions Gather or Push Beasts"?
Nearly. In theory it could include some other sort of action that said "Target Spirit may Push a Beasts" or "Each Spirit Pushes a Beasts"... but in practice no such things exist, so functionally speaking it's identical.
("Each player may Push a Beasts" would not be sufficient - cases like that don't represent Spirits doing things, the game just needs a player to make a decision for a Fear or Event card. It would have to use the word "Spirit".)
Usually, the wording "when you (do X)" is used for your pieces or other game components: e.g., "when you Forget a Power Card" or "when you uncover this spot on your Presence track" or "when your Presence is destroyed". Those can obviously happen as a result of many different sorts of actions, not only your own.
