
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 an arithmetic sequence ${a_n}$ is $S_n$, and the geometric sequence ${b_n}$ satisfies $a_1 = b_1 = 1$, $S_3 = b_3 + 2$, and $S_5 = b_5 - 1$.

(I) Find the general terms of the sequences ${a_n}$ and ${b_n}$;

(II) If the sequence ${b_n}$ is increasing, find the sum of the first $n$ terms of the sequence ${a_n b_n}$, denoted as $T_n$.

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