
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Let \( g(x) \) be a function piecewise defined as 
\[
g(x) = \left\{
\begin{array}{cl}
-x+2 & \text{if } x \leq 0, \\
3x-50 & \text{if } x > 0.
\end{array}
\right.
\]
If \( a \) is negative, find \( a \) such that \( g(g(g(15))) = g(g(g(a))) \).

Present the answer in LaTex format: \boxed{Your answer}
user