
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
In an arithmetic sequence $\{a_n\}$, $a_2=6$ and $a_3+a_6=27$.
(1) Find the general form of the sequence $\{a_n\}$.
(2) If the general form of sequence $\{b_n\}$ is $b_{n}=3^{n-1}$, find the sum of the first $n$ terms of the product sequence $\{a_n \cdot b_n\}$, denoted $T_n$.

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