
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 conical frustum-shaped, upward-widening 1-liter household measuring cup has the 1/2 liter mark located at 2/3 of the height of the cup. What is the ratio of the diameters of the base circle to the top circle?

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