
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
The roots of the polynomial  $P(x) = x^4 -10x^3 + 35x^2 -51x + 26$  form the side lengths of a quadrilateral. The maximum area of such a quadrilateral is of the form  $\sqrt{n}$  for some positive integer  $n$ . Find  $n$ .

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