
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
Line segments are drawn from the vertex opposite the hypotenuse of a right triangle to the points that quadrisect the hypotenuse of the triangle. The lengths of these line segments are $\sin x$ and $\cos x$, where $x$ is a real number such that $0 < x < \frac{\pi}{2}$. If $\sin x$ is the segment to the closest quarter point from one end of the hypotenuse and $\cos x$ is to the next closest quarter point, determine the length of the hypotenuse.
A) $\frac{2\sqrt{5}}{5}$
B) $\frac{\sqrt{7}}{2}$
C) $\frac{2\sqrt{5}}{3}$
D) $\frac{4\sqrt{2}}{3}$
E) $\frac{2\sqrt{3}}{3}$

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