
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 polynomial of degree 2008 with leading coefficient 1 such that
\[ P(0) = 2007, \; P(1) = 2006, \; P(2) = 2005, \ldots, P(2007) = 0. \]
Determine the value of \( P(2008) \). You may use factorials in your answer.

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