
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
Two cones, $X$ and $Y$, have different dimensions. If the radius of the base and height of cone $X$ is 10 cm and 15 cm respectively, and those for cone $Y$ are 15 cm and 10 cm respectively, what is the ratio of the volume of cone $X$ to the volume of cone $Y$? Express your answer as a common fraction.

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