
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
A geometric sequence $\{a\_n\}$ has the sum of its first $n$ terms $S\_n=2^{n+6}-a$. Another sequence $\{b\_n\}$ satisfies $b\_n= \frac {1}{n}(\log\_2a\_1+\log\_2a\_2+…+\log\_2a\_n) (n∈N^{∗})$.
(1) Find the value of $a$ and the general term formula of $\{a\_n\}$;
(2) Find the sum of the first $n$ terms of the sequence $\{ \frac {1}{b\_n \cdot b_{n+1}}\}$;
(3) Find the minimum value of the sequence $\{ \frac {a\_n}{b\_n}\}$.

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