
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
An engineer is designing a clock face and wants the hour hand to point to 7 hours in reference to noon at the top. Calculate the cosine of the angle the hour hand makes with the 12-hour position in standard counterclockwise measurement, and determine the horizontal displacement of the tip of the hour hand from the centre of the clock, assuming the clock has a radius of 15 units.

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