
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
Let \( ABCD \) be a rectangle with \( AB = 3 \) and \( BC = 7 \). Let \( W \) be a point on segment \( AB \) such that \( AW = 1 \). Let \( X, Y, Z \) be points on segments \( BC, CD, DA \), respectively, so that quadrilateral \( WXYZ \) is a rectangle, and \( BX < XC \). Determine the length of segment \( BX \).

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