
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
Three cones, $A$, $B$, and $C$, have the following dimensions: Cone $A$ has a radius of 10 units and a height of 20 units, Cone $B$ has a radius of 20 units and a height of 40 units, and Cone $C$ has a radius of 15 units and a height of 30 units. What is the ratio of the volume of cone $A$ to the volume of cone $C$? Express your answer as a common fraction.

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