
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 the polynomial
$$
\begin{aligned}
& (1+x)+(1+x)^{2}+(1+x)^{3}+\cdots+(1+x)^{n} \\
= & b_{0}+b_{1} x+b_{2} x^{2}+\cdots+b_{n} x^{n},
\end{aligned}
$$

and $b_{1}+b_{2}+\cdots+b_{n}=1013$, find a possible value of the positive integer $n$.

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