
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 S_n is the sum of the first n terms of \{a_n\}, it is known that a_2 = 9 and S_5 = 65.
(1) Find the general formula for the n-th term of the sequence \{a_n\};
(2) Suppose the sum of the first n terms of the sequence \{\frac{1}{S_n - n}\} is T_n, find T_n.

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