
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
Find polynomials \(a(x)\), \(b(x)\), \(c(x)\) such that
\[
|a(x)| - |b(x)| + c(x) =
\begin{cases} 
 -1 & \text{for } x < -1, \\ 
 3x + 2 & \text{for } -1 \leq x \leq 0, \\ 
 -2x + 2 & \text{for } x > 0.
\end{cases}


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