
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 the sequence ${a_n}$ has a general term given by $a_n=2^{n-1}+1$, find the value of $a_1\binom{n}{0}+a_2\binom{n}{1}+a_3\binom{n}{2}+\ldots+a_{n+1}\binom{n}{n}$.

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