
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 polynomial
\[P(x)=x^3+3x^2+6x+10.\]
Let its three roots be  $a$ ,  $b$ ,  $c$ . Define  $Q(x)$  to be the monic cubic polynomial with roots  $ab$ ,  $bc$ ,  $ca$ . Compute  $|Q(1)|$ .

*Proposed by Nathan Xiong*

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