
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
Let \( P(x)=x^4 + 2x^3 - 13x^2 - 14x + 24 \) be a polynomial with roots \( r_1, r_2, r_3, r_4 \).
Let \( Q \) be the quartic polynomial with roots \( r_1^2, r_2^2, r_3^2, r_4^2 \), such that the coefficient of the \( x^4 \) term of \( Q \) is 1.
Simplify the quotient \( \frac{Q(x^2)}{P(x)} \), leaving your answer in terms of \( x \). (You may assume that \( x \) is not equal to any of \( r_1, r_2, r_3, r_4 \)).

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