
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 a radius of 10 units, two chords PQ and RS intersect at point T, such that T bisects PQ. Given that PT=8 units, and PQ is the only chord starting from P which is bisected by RS, find the sine of the central angle subtended by arc PR. Assume that this sine value can be represented as a fraction $\frac{m}{n}$ in its lowest terms. What is the product $mn$?

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