
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
The lateral surface of a truncated cone is painted blue up to half of its lateral height and red above that. The blue surface area is twice the size of the red surface area. How many times the radius of the base circle is the radius of the top circle?

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