
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 polynomial with \( P(1) = P(2) = \cdots = P(2007) = 0 \) and \( P(0) = 2009! \). \( P(x) \) has leading coefficient 1 and degree 2008. Find the largest root of \( P(x) \).

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