"Explicit needed action or explicit action needed"
The phrase "explicit action needed is correct". The former one doesn't make sense.
In the correct phrase, the adjective "explicit" modifies "action" and the adjective "needed" modifies "explicit action".
However, I also agree with CarSmack that we can say "the needed explicit action".
In this phrase also, the adjective "explicit" modifies action and the other adjective "needed" modifies "explicit action". In grammar, the adjective that modifies a noun and the adjective that modifies a paired phrase (adj + noun) are called cumulative adjectives. In order to decide as to which phrase is correct, we put "and" between these adjectives, rearrange their order and see which phrase makes sense and which phrase makes no sense. The phrase that makes sense will be considered to be correct.
As both the phrases "the needed explicit action and the explicit action needed" make sense, we can use either of them.