
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 $S\_2$, and volumes $V\_1$ and $V\_2$, respectively. If their lateral areas are equal and $\frac{S\_1}{S\_2} = \frac{9}{4}$, find the value of $\frac{V\_1}{V\_2}$.

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