
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
Given a quadratic equation \( Dx^2 + Ex + F = 0 \) with roots \( \alpha \) and \( \beta \), find the value of \( p \) such that the roots of the equation \( x^2 + px + q = 0 \) are \( \alpha^2 + 1 \) and \( \beta^2 + 1 \).

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