
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 a geometric sequence $\{a\_n\}$ is $S\_n$, and $6S\_n=3^{n+1}+a (n∈N^{+})$,
(1) Find the value of $a$ and the general term formula of the sequence $\{a\_n\}$;
(2) Let $b\_n=(1-an)log _{3}(a\_n^{2}⋅a_{n+1})$, find the sum of the first $n$ terms of $\{ \frac {1}{b\_n}\}$, denoted as $T\_n$.

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