Prayer is ALWAYS appropriate.
Not necessarily.
God does not do what He has appointed for you to do for yourself and others.
It is a sin to refuse to execute the duties my Heavenly Father has set before me. In this case it is certain that not only will He not hear my prayers (Ps. 66:18), but He may well allow the heaping of even more negative consequences arising from my refusal to accept the responsibility to act; resorting only to requests for a Providential solution when my action is the practical answer that solves the problem.
It is precisely that shirking of the task at hand which causes adversaries to identify ineffective appeals to God as a cop-out, as a substitute for applying obvious remedies.