
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 positive geometric sequence, $a\_2=3$, $a\_6=243$, and $S\_n$ is the sum of the first $n$ terms of the arithmetic sequence $\{b\_n\}$, $b\_1=3$, $S\_5=35$.
(1) Find the general term formulas for $\{a\_n\}$ and $\{b\_n\}$.
(2) Let $T\_n = a\_1b\_1 + a\_2b\_2 + ... + a\_n b\_n$, find $T\_n$.

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