
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 the terms of the geometric sequence $\{a\_n\}$ are all positive, and $2a\_1+3a\_2=1$, $a\_3^2=9a\_2a\_6$, and the arithmetic sequence $\{b\_n\}$ satisfies $b\_2=0$, $b\_6+b\_8=10$.
(I) Find the general terms of the sequences $\{a\_n\}$ and $\{b\_n\}$;
(II) Find the sum of the first $n$ terms of the sequence $\{a\_n \cdot b\_n\}$, denoted as $S\_n$.

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