
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 that $\{a_n\}$ is a geometric sequence with a common ratio not equal to $1$, and $S_n$ is the sum of the first $n$ terms of the sequence $\{a_n\}$, with $a_3=3$ and $S_3=9$  
(Ⅰ) Find the general formula for the sequence $\{a_n\}$;  
(Ⅱ) Let $b_n=\log_2 \frac{3}{a_{2n+3}}$, if $c_n= \frac{4}{b_nb_{n+1}}$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, $T_n$.

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