
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
Let S$_n$ be the sum of the first n terms of the arithmetic sequence {a$_n$}, with S$_9$=81 and a$_2$+a$_3$=8.
(1) Find the general term formula for {a$_n$};
(2) If S$_3$, a$_{14}$, S$_m$ form a geometric sequence, find S$_{2m}$.

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