
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 points dividing the hypotenuse into four equal segments. The lengths of these segments from the vertex to the points are $\sin \frac{\pi}{4}$ and $\cos \frac{\pi}{4}$. Determine the length of the hypotenuse.

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