
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
Given the function $f(x) = $
$$
\begin{cases}
2^{x-1} - 2 & ,x \geq 1 \\
2^{1-x} - 2 & ,x < 1
\end{cases}
$$
Find the solution set for the inequality $f(x-1) \leq 0$.

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