
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  $P$  be a cubic monic polynomial with roots  $a$ ,  $b$ , and  $c$ .  If  $P(1)=91$  and  $P(-1)=-121$ , compute the maximum possible value of \[\dfrac{ab+bc+ca}{abc+a+b+c}.\]

*Proposed by David Altizio*

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