
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
Given an arithmetic sequence \(\{a_n\}\) where \(a_2=6\) and \(a_3+a_6=27\):
1. Find the general term formula for the sequence \(\{a_n\}\).
2. Let \(S_n\) denote the sum of the first \(n\) terms of the sequence \(\{a_n\}\). Calculate the sum of the first \(n\) terms, \(T_n\), for the sequence \(\left\{ \frac{1}{S_n} \right\}\).

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