
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 being $S_n$. It is known that $S_{10} = 120$ and the sequence $a_2 - a_1, a_4 - a_2, a_1 + a_2$ forms a geometric sequence.
(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 {$$\frac{1}{S_n}$$}, find the smallest value of $n$ such that $T_n > \frac{15}{22}$.

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