
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 of degree \( n \) satisfying
$$
P(k)=\binom{n+1}{k}^{-1} \quad \text { for } k=0,1, \ldots, n.
$$

Determine \( P(n+1) \).

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