
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
Let $(1+x) + (1+x^2) +\ldots+ (1+x)^n = a_0 + a_1x + \ldots + a_{n-1}x^{n-1} + a_nx^n$. If $a_{n-1} = 2009$, find the sum $a_0 + a_1 + \ldots + a_{n-1} + a_n$ in the form of $\beta^a - \lambda$.

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