
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 located on a circle with radius $8$, and the chord $PQ$ has a length of $10$. Point $R$ is the midpoint of the minor arc $PQ$. Determine the length of the line segment $PR$.
**A)** $\sqrt{113}$ **B)** $\sqrt{118}$ **C)** $\sqrt{123}$ **D)** $\sqrt{128 - 16\sqrt{39}}$

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