
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  $\{a_n\}$  be a sequence satisfying:  $a_1=1$  and  $a_{n+1}=2a_n+n\cdot (1+2^n),(n=1,2,3,\cdots)$ . Determine the general term formula of  $\{a_n\}$ .

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