
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 the arithmetic sequence $\left\{ a_n \right\}$, $a_2=6$, $a_3+a_6=27$.

(1) Find the general formula for the sequence $\left\{ a_n \right\}$;

(2) If the general formula for the sequence $\left\{ b_n \right\}$ is $b_n=3^{n-1}$, find the sum of the first $n$ terms $T_n$ of the sequence $\left\{ a_n \cdot b_n \right\}$.

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