
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
Let the sum of the first $n$ terms of an arithmetic sequence {${a_n}$} be $S_n$, and suppose $a_2 = 5$, $S_5 = 35$. Consider a sequence {${b_n}$} such that $a_n = \log_2 b_n$.
(1) Find the general term formula for the sequence {${a_n}$}.
(2) Find the sum of the first $n$ terms of the sequence {${b_n}$}, denoted $T_n$.
(3) Let $G_n = a_1 \cdot b_1 + a_2 \cdot b_2 + \ldots + a_n \cdot b_n$. Calculate $G_n$.

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