
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
Given that $\{a_n\}$ is an arithmetic sequence with common difference $d$, and $n \in \mathbb{N}$, simplify the polynomial

$$
p_n(x) = a_0 \binom{n}{0} (1-x)^n + a_1 \binom{n}{1} x(1-x)^{n-1} + a_2 \binom{n}{2} x^2 (1-x)^{n-2} + \cdots + a_n \binom{n}{n} x^n
$$

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