
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 face with a radius of $30$ cm and a smaller circular disk with a radius of $15$ cm, determine the position on the clock face where the disk is tangent when the arrow is next pointing rightward after rolling from the $3$ o'clock position on the clock face clockwise without slipping.

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