
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, vertex $A$ is opposite the hypotenuse $BC$. The hypotenuse is bisected at points $D$ and $E$, with $D$ closer to $B$ and $E$ closer to $C$. The segment lengths $AD$ and $AE$ from the vertex to these midpoint segments are $\tan x$ and $\cot x$ respectively, where $x$ is an angle such that $0 < x < \frac{\pi}{2}$. Determine the length of the hypotenuse $BC$.

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