
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
Let \(O\) be the center of circle \(C\) with radius \(10\), and let \(Q\) be a point inside \(C\) such that \(OQ = 8\). Consider all lines through \(Q\) that intersect \(C\), forming chords of \(C\), and determine the locus of the midpoints of these chords.
A) A circle with radius 4 \\
B) A circle with radius 8 \\
C) A semicircle with radius 4 \\
D) A semicircle with radius 8 \\
E) None of the above

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