
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 the sequence $\{a\_n\}$, where $a\_n > 0$, $a\_1=2$, $a\_4=16$, and $a\_n^{2}=a\_{n-1}a\_{n+1}$:

1. Find the general term formula for the sequence $\{a\_n\}$;
2. Let $b\_n=\log \_{2}a\_{n}$, $c\_n= \frac {1}{b\_n b\_{n+1}}$, find the sum of the first $n$ terms $T\_n$ of the sequence $\{c\_n\}$.

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