
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
Let $\{a_n\}$ be an arithmetic sequence with the sum of the first $n$ terms denoted as $S_n$, and let $\{b_n\}$ be a geometric sequence. Given $a_1=3$, $b_1=2$, $b_2+S_2=16$, and $2b_2-a_6=3$,

$(1)$ Find the general term formulas for sequences $\{a_n\}$ and $\{b_n\}$;

$(2)$ Let $c_n= \frac {1}{a_n\cdot \log_2 b_n}$, 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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