
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 $S\_n$, where $n∈N^∗$, $a\_3=5$, and $S\_10=100$.

(1) Find the general term formula of the sequence ${a\_n}$.
(2) Let ${b\_n} = 2^{a\_n} + a\_n \cdot \sin^2{\frac{n\pi}{2}}$. Find the sum of the first $n$ terms of the sequence ${b\_n}$, denoted as $T\_n$.

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