
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 two cylinders, A and B, with base areas $S_1$ and $S_2$ respectively, and $\frac{S_1}{S_2} = \frac{9}{4}$. Their volumes are $V_1$ and $V_2$ respectively. If their lateral surface areas are equal, then $\frac{V_1}{V_2} = $ \_\_\_\_\_\_.

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