
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 sequence $\{a_n\}$ with the general term formula $a_n = 2^{n-1} + 1$, find the value of $a_1C_n^0 + a_2C_n^1 + a_3C_n^2 + \ldots + a_{n+1}C_n^n$.

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