
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
The sequence $\{a_n\}$ is an arithmetic sequence with the sum of its first $n$ terms denoted by $S_n$. The sequence $\{b_n\}$ is a geometric sequence such that $a_1 = 3$, $b_1 = 1$, $b_2 + S_2 = 10$, and $a_5 - 2b_2 = a_1$.

(1) Find the general term formulas for the sequences $\{a_n\}$ and $\{b_n\}$.

(2) Let $c_n = a_n \cdot b_n$. Denote the sum of the first $n$ terms of the sequence $\{c_n\}$ by $T_n$. Find $T_n$.

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