
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
From the first equation we get:

\[ P = -\frac{x^{2}-x-2}{x-1} = -x + \frac{2}{x-1}, \quad x \neq 1 \]

From the second equation we get: 

\[ p = -\frac{x^{2}+2x-1}{x+2} = -x + \frac{1}{x+2}, \quad x \neq -2 \]

Then, if \( x \) is a common root corresponding to parameter \( p \), we have:

\[ -x + \frac{2}{x-1} = -x + \frac{1}{x+2} \]

From this we find \( x = -5 \) and \( p = \frac{14}{3} \).

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