
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
The terms of the geometric sequence $\{a_n\}$ are all positive, and $2a_1+3a_2=1$, $a_3^2=9a_2a_6$.  
(1) Find the general formula for the sequence $\{a_n\}$.  
(2) Let $b_n=\log_{3}a_1+\log_{3}a_2+\ldots+\log_{3}a_n$, and if $c_n=-\frac{1}{b_n}$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, $S_n$.

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