
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
A cylinder and a cone entirely fit inside it are given. Calculate the ratio of the volume of the cone to the volume of the cylinder. The cylinder has a height of 10 cm and radius of 5 cm. The cone has a height of 5 cm but retains the same radius as the cylinder.

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