
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
Consider two circular disks: a larger disk with a radius of $30$ cm fixed in place, and a smaller rolling disk with a radius of $15$ cm. The smaller disk, initially tangent to the larger disk at the topmost point ($12$ o' clock), starts rolling clockwise along the edge of the larger disk. The smaller disk has an arrow painted pointing upwards initially. Calculate at what position on the larger disk the smaller one will again be tangent when the arrow points upward for the first time after completing its roll.

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