
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 that $S\_n$ represents the sum of the first $n$ terms in a geometric sequence ${a\_n}$, and $S\_3 = \frac{7}{2}$, $S\_6 = \frac{63}{16}$.

(1) Find the expression for ${a\_n}$;
(2) If ${b\_n} = \frac{1}{{a\_n}} + n$, find the sum of the first $n$ terms in the sequence ${b\_n}$, denoted as ${T\_n}$.

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