
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

Determine the coefficients \(a_{0}, a_{1}, a_{2}, \ldots, a_{n}\) such that the polynomial

\[ (1+x) - \left(a_{0} + a_{1} x + \ldots + a_{n} x^{n}\right)^{2} \]

is divisible by \(x^{n+1}\).

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