
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
Points \(P\) and \(Q\) are on a circle of radius \(8\) where the chord \(PQ = 10\). Point \(R\) is the midpoint of the minor arc \(PQ\). Calculate the length of the line segment \(PR\).
A) \(8\sin\left(\frac{1}{2}\cos^{-1}\left(\frac{16}{20}\right)\right)\)
B) \(\sqrt{81}\)
C) \(8\sin\left(\frac{1}{2}\cos^{-1}\left(\frac{25}{32}\right)\right)\)
D) \(\sqrt{136}\)
E) \(8\)

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