
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
In a cylinder with a radius of 4 cm and a height of 18 cm, two cones are placed. The first cone has a radius of 4 cm and a height of 6 cm, and it is placed right-side-up. The second cone, which is placed upside-down, has the same radius of 4 cm but a height of 9 cm. Find the ratio of the total volume of the two cones to the volume of the cylinder. Express your answer as a common fraction.

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