
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
A polynomial \( P \) of degree \( n \in \mathbb{N} \) satisfies:

$$
\text{for } k = 0, 1, \ldots, n, \quad P(k) = \frac{k}{k+1}
$$

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

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