
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
Let the base areas of two cylinders be $S_1$ and $S_2$, and their volumes be $\upsilon_1$ and $\upsilon_2$, respectively. If their lateral areas are equal, and $$\frac {S_{1}}{S_{2}}= \frac {16}{9},$$ then the value of $$\frac {\upsilon_{1}}{\upsilon_{2}}$$ is \_\_\_\_\_\_.

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