
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<sub>n</sub> = 3<sup>n-1</sup>, $${{b}_{n}}=\frac{{{6}^{n}}}{2{{a}_{n}}}$$, and the sum of the first n terms of the sequence {b<sub>n</sub>} is S<sub>n</sub>, find S<sub>9</sub> (answer with a concrete number).

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