
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 right triangle $PQR$ with $PQ$ being the hypotenuse, points $S$ and $T$ are placed such that $S$ bisects $PQ$ and $T$ divides $PQ$ into segments in the ratio 1:3 from $P$. If the lengths from $R$ to $S$ and $T$ are $\sin y$ and $\cos y$, respectively, where $y$ is such that $0 < y < \frac{\pi}{2}$, determine the length of the hypotenuse.
A) $\frac{8}{15}$
B) $\frac{8\sqrt{5}}{15}$
C) $\frac{16\sqrt{5}}{15}$
D) $\frac{5\sqrt{5}}{8}$
E) $\frac{3\sqrt{5}}{5}$

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