Q: When can a character perform actions during a phase?
For example, if an investigator with the Ally Duke (“Discard
to immediately restore your Sanity to its maximum.”) draws an
encounter and has to roll a die and lose that much Sanity, when
can he discard Duke to restore Sanity?

A: An action can be performed at any time during the listed phase,
as long as its conditions are met. However,
once an encounter is
drawn, it must be resolved before any actions can be performed.
In the example with Duke, the player could use his ability either
before drawing the encounter card or after the drawn card’s effects
are resolved, but not between drawing the card and resolving it.
So, if the player does not use Duke before drawing the card, and
the drawn card inflicts Sanity loss that reduces the investigator to
0 Sanity, the investigator goes insane before he can use Duke.

Imploded, Retainer... И шо, так таки нельзя?