
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
Given a large circular clock with a radius of $30$ cm and a smaller circular disk with a radius of $15$ cm externally tangent to the clock face at the $6$ o'clock position, determine the point on the clock face where the disk will be tangent when its arrow points vertically downward again after rolling clockwise without slipping.

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