
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 a sequence ${a_n}$ whose first $n$ terms sum is $S_n = nb_n$, where ${b_n}$ is an arithmetic sequence with the first term $1$ and a common difference $2$.

(I) Find the general formula for the sequence ${a_n}$.

(II) If ${c_n} = \frac{1}{a_n(2b_n+3)}$, find the first $n$ terms sum $T_n$ for the sequence ${c_n}$.

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