Why should it be broken? It's just a slightly more reliable Lookout with the +1 Action replaced by some inverse Pearl Diving
...and a +card.
Let's compare it with Masquerade, one of the strongest cards in the game:
Masquerade:
+ Safer (chooses the worst one out of 6 cards to trash, know 4 options before playing the card)
+ Can sometimes luck out and receive a good card in exchange for a bad card
Inspire:
+ Leaves you with a better hand for this turn
+ Smaller chance of terminal collision
+ Leaves you with a better deck for the remaining turns this shuffle
+ Some control over getting a good turn now vs. getting a good turn next turn
+ Cycles more cards
+ Triggers more wanted reshuffles
- Triggers more unwanted reshuffles
Looks like broken.