Can I declare I am using the Drum 'at the start of the move phase' then actually use it later in the phase?

Then it would be like using Might for Heroic March: declare it before the Move phase, then move models I don't want affected by the March, then the Hero actually does the March action.

I'm not terribly familiar with the practical use of wardrums, but from the wording of the rule on pg 89 it looks like the effect is instantly applied once the drum is sounded at the start of the phase and not when the drummer activates later on like with heroic march. Therefore, all models with the key word that are in range of the drum would have to be effected by it during their individual moves, regardless of move order.

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