
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 $\{a_n\}$ with the sum of its first $n$ terms denoted as $S_n$, and it is known that $a_1 + a_3 = 10$ and $S_4 = 24$.

(1) Find the general term formula for the sequence $\{a_n\}$.

(2) Find the sum of the first $n$ terms, denoted as $T_n$, for the sequence $\{\frac{1}{S_n}\}$.

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