
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 sector representing a quarter of a circle is cut out from the circle. The lateral surfaces of two cones are made from this sector and the remaining part of the circle. Find the ratio of the heights of these cones.

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