
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
 $P\left(x\right)$  is a polynomial of degree at most  $6$  such that such that  $P\left(1\right)$ ,  $P\left(2\right)$ ,  $P\left(3\right)$ ,  $P\left(4\right)$ ,  $P\left(5\right)$ ,  $P\left(6\right)$ , and  $P\left(7\right)$  are  $1$ ,  $2$ ,  $3$ ,  $4$ ,  $5$ ,  $6$ , and  $7$  in some order. What is the maximum possible value of  $P\left(8\right)$ ?

*2018 CCA Math Bonanza Individual Round #13*

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