
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 $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, and it is given that $S_{n}= \frac {1}{2}\cdot 3^{n}+ \frac {3}{2}$.
(1) Find the general term formula for the sequence ${a_{n}}$;
(2) If the sequence ${b_{n}}$ satisfies $a_{n}b_{n}=\log _{3}a_{n}$, find the sum of the first $n$ terms $T_{n}$ of the sequence ${b_{n}}$.

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