
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
A sequence ${a_n}$ has a sum of its first $n$ terms denoted as $S_n$.
(1) When ${a_n}$ is a geometric sequence with $a_1 = 1$ and $\frac{1}{a_1}$, $\frac{1}{a_3}$, $\frac{1}{a_4} - 1$ form an arithmetic sequence, find $a_n$.
(2) If ${a_n}$ is an arithmetic sequence and $S_1 + a_2 = 3$, $S_2 + a_3 = 6$, find the sum: $T_n = \frac{1}{S_1} + \frac{1}{S_2} + \frac{1}{S_3} + ... + \frac{1}{S_n}$.

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