
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
In a semicircle, square $ABCD$ is drawn with its side $AB$ aligned along the diameter of the semicircle. The semicircle and square $ABCD$ are coplanar. The length of line segment $AB$ is 8 centimeters. If point $M$ is located one-quarter of the way along the arc from $A$ to $B$, what is the length of segment $MC$? Express your answer in simplest radical form.

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