Help with a complex Update

I have a table of users and a table of user_actions.
I'd like to have a first_action column in the user table. 

How would I go about updating that info.

I'd immagine it'd be something like this:

update user_info set first_action = (select min(action_timestamp) from 
action_info where user_id = ?? current user id ??);

Is this possible or do I have to make an external for loop?
       Orion