
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 that {$a_n$} is a geometric sequence with $a_1 = 1$ and $a_6 = 243$. $S_n$ is the sum of the first $n$ terms of the arithmetic sequence {$b_n$}, with $b_1 = 1$ and $S_5 = 25$.
(1) Find the general term formulas for {$a_n$} and {$b_n$};
(2) Let $T_n = a_1b_1 + a_2b_2 + \ldots + a_nb_n$, find $T_n$.

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