Given an initial sequence \(a_1, a_2, \ldots, a_n\) of real numbers, we perform a series of steps. 
At each step, we replace the current sequence \(x_1,x_2,\ldots,x_n\)
with the sequence \(|x_1-a|,|x_2-a|,\ldots,|x_n-a|\) for some number \(a\) that can vary with each step.

(a) Prove that no matter what sequence we start with, there is some way to do steps to reach the sequence \(0,0,\ldots,0\).

(b) * Determine (with proof) the maximum, over all sequences of length \(n\), of the minimum number of steps required to reach \(0,0,\ldots,0\).