
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 smaller disk rolls counterclockwise around the larger circular clock with a radius of $30$ cm and a smaller circular disk with a radius of $15$ cm, which starts externally tangent to the clock face at the $12$ o'clock position, with an arrow on the disk pointing upward. Determine the point on the clock face at which the disk will be tangent when the arrow is next pointing in the upward vertical direction.

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