
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  $P(x) = x^3 + 8x^2 - x + 3$  and let the roots of  $P$  be  $a, b,$  and  $c.$  The roots of a monic polynomial  $Q(x)$  are  $ab - c^2, ac - b^2, bc - a^2.$  Find  $Q(-1).$ 

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