
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 the sum of the first $n$ terms of the sequence ${a_n}$ is $S_n = n^2$, and ${b_n}$ is a geometric sequence with $b_1 = a_1$ and $b_4$ being the arithmetic mean of $a_4$ and $a_5$.
1. Find the general term formulas for the sequences ${a_n}$ and ${b_n}$.
2. Let $c_n = a_n \cdot b_n$, find the sum of the first $n$ terms of the sequence ${c_n}$, denoted as $T_n$.

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