
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
Consider the equation \( x^{3}-(a+2) x^{2}+(2a+1) x-a=0 \) with roots \( x_{1}, x_{2}, x_{3} \). It is given that

\[ \frac{2}{x_{1}} + \frac{2}{x_{2}} = \frac{3}{x_{3}}. \]

Solve the equation.

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