
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 a non-zero common difference arithmetic sequence ${a_n}$ with the sum of its first $n$ terms as $S_n$, $a_2 + a_5 = 21$, and $a_1, a_3, a_9$ form a geometric sequence in order.

1. Find the general term formula for the sequence ${a_n}$;
2. Find the sum $T_n$ of the first $n$ terms for the sequence ${\frac{1}{S_n}}$.

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