
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 circular clock face with a radius of $30$ cm and a smaller disk with a radius of $15$ cm externally tangent to the clock face at $3$ o'clock, find the point on the clock face where the disk will be tangent when its arrow is next pointing in the right (horizontal) direction again.

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