
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
For a positive integer $n$, define an operation "$\ast$" that satisfies the following properties: (1) $1 \ast 1 = 2$; (2) $(n+1) \ast 1 = n \ast 1 + 2^{n+1}$. Express $n \ast 1$ using an algebraic expression involving $n$.

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