
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
Determine \( p \) such that the equation

\[
\frac{2\left(1-p+p^{2}\right)}{1-p^{2}} x^{2}+\frac{2-p}{1+p} x-\frac{p}{1-p}=0
\]

has \( x=-1 \) as a root.

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