
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
Construct a quadratic equation whose roots ($x_{1}$ and $x_{2}$) satisfy the following relations:

\[ x_{1} x_{2} + x_{1} + x_{2} - a = 0, \]
\[ x_{1} x_{2} - a(x_{1} + x_{2}) + 1 = 0. \]

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