
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
Consider the arithmetic sequence $\{a_n\}$ with $a_3 = 5$ and $a_5 - 2a_2 = 3$. Additionally, consider the geometric sequence $\{b_n\}$ with first term $b_1 = 3$ and common ratio $q = 3$.

1. Find the general term formula for both sequences $\{a_n\}$ and $\{b_n\}$.
2. Let $c_n = a_n \cdot b_n$, and let $T_n$ denote the sum of the first $n$ terms of the sequence $\{c_n\}$. Find $T_n$.

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