
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, two intersecting chords $PQ$ and $RS$ are given such that $PQ=10$ and $RS$ bisects $PQ$ at point $T$. It is also given that $PQ$ is the only chord starting at $P$ which is bisected by $RS$. Determine the sine of the central angle subtended by the minor arc $PR$ and express it as a fraction $\frac{a}{b}$ in lowest terms. Find the product $ab$.

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