
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 \( p(x) \) of degree \( n \) satisfies the conditions \( p(0) = 0 \), \( p(1) = \frac{1}{2} \), \( p(2) = \frac{2}{3} \), ..., \( p(n) = \frac{n}{n+1} \). Find \( p(n+1) \).

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