
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 positive arithmetic geometric sequence $\{a_n\}$ with a common ratio of $q$, the sum of the first $n$ terms is $S_n$, and it satisfies $a_2a_4=64$, $S_3=14$. Let $$b_{n}=log_{2}a_{n}(n∈N^{*})$$.
(1) Find the values of $a_1$, $a_2$ and the general term formula of the sequence $\{a_n\}$;
(2) Determine whether the sequence $\{b_n\}$ is an arithmetic sequence and explain the reason;
(3) Let $$c_{n}= \frac {1}{b_{n}b_{n+1}}$$, 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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