
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
Determine the general term formula for the sequence $\{a_n\}$ whose terms are distinct and form an arithmetic progression, given that $a_3a_5 = 3a_7$ and $S_3 = 9$.
(1) Find the general term formula for the sequence $\{a_n\}$.
(2) Let $T_n$ be the sum of the first n terms of the sequence $\left\{\frac {1}{a_n a_{n+1}}\right\}$.

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