
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

Using a compass, draw a circle. Without changing the radius on the compass, mark six distances along the circumference equal to the circle's radius (measuring these distances not along the arc, but along the chord). If done accurately, the last point will coincide with the starting point. Why?

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