
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 general term formulas of the sequences $\{a\_n\}$ and $\{b\_n\}$ as $a\_n=2^n$ and $b\_n=3^n$ respectively. If $c\_n=a\_1b\_n+a\_2b\_{n-1}+a\_3b\_{n-2}+ \cdots + a\_nb\_1$, find the general term formula of the sequence $\{c\_n\}$.

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