
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 \( p(x) \) be a monic polynomial of degree 7 such that \( p(1) = 2, \) \( p(2) = 3, \) \( p(3) = 4, \) \( p(4) = 5, \) \( p(5) = 6, \) \( p(6) = 7, \) and \( p(7) = 8. \) Find \( p(8). \)

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