
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 \( \mathrm{P} \) be a polynomial of degree 2008 such that for every integer \( \mathrm{k} \in \{1, \ldots, 2009\} \), \( \mathrm{P}(\mathrm{k}) = \frac{1}{k} \). Calculate \( P(0) \).

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