
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 geometric sequence $\{a_n\}$ satisfies $a_1a_6=32a_2a_{10}$, and the sum of the first $3$ terms of $\{a_n\}$, $S_3= \frac {21}{4}$.  
$(1)$ Find the general formula for the sequence $\{a_n\}$.  
$(2)$ Let the sequence $b_n=\log_2 \frac {a_n}{3}$, find the sum of the first $n$ terms of $\{b_n\}$, $T_n$.

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