
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 circular clock face has a radius of $30$ cm and a small disk with a radius of $5$ cm, externally tangent to the clock at the 12 o'clock position. After the disk makes three complete rotations without slipping, determine the position on the clock face where the disk is tangent when the arrow painted on it points directly upwards.

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