
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 circle with radius 7 units, two chords PQ and RS intersect such that RS bisects PQ at point T. Given that PQ = 14 units, and RT = 5 units, determine the sine of the central angle subtending arc PR. Assume that PQ is the only chord starting at P bisected by RS. Express the result as a reduced fraction \(\frac{m}{n}\) and find \(mn\).

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