
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 sequence ${b_n}$ is an arithmetic sequence with first term 1, and sequence ${a_n}$ satisfies $a_{n+1} - 3a_n - 1 = 0$, with $b_3 + 1 = a_2$ and $a_1 = 1$.
(I) Find the general term formula for sequence ${a_n}$;
(II) Let $c_n = a_n b_n$, find the sum of the first n terms $T_n$ for sequence ${c_n}$.

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