Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: Let $g(x)$ be a function piecewise defined as \[g(x) = \left\{
\begin{array}{cl}
-x & x\le 0, \\
2x-41 & x>0.
\end{array}
\right.\] If $a$ is negative, find $a$ so that $g(g(g(10.5)))=g(g(g(a)))$.
user