
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 $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, and it is known that $\frac{8}{a_1} + \frac{6}{a_2} = \frac{5}{a_3} > 0$, $S_6= \frac{63}{32}$  
$(1)$ Find the general formula for the sequence $\{a_n\}$  
$(2)$ If $b_n=-\log_2 a_n$, $c_n=a_n b_n$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, denoted as $T_n$．

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