
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 $\left\{a_{n}\right\}$ has its first term as 2, and the sum of the first $n$ terms is denoted by $S_{n}$. The sequence $\left\{S_{n}\right\}$ forms a geometric sequence with a common ratio of $\frac{1}{3}$.
1. Find the general term formula for the sequence $\left\{a_{n}\right\}$.
2. Let $b_{n}=a_{n} S_{n}$, find the sum of the terms of the sequence $\left\{S_{n}\right\}$.

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