
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 regular trapezoid \(ABCD\) where \(AB \parallel DC\) and \(AD = BC\), find \(CY = DX\). The points \(X\) and \(Y\) are endpoints of a line \(XY\) that divides the trapezoid into two trapezoids \(ABYX\) and \(XYCD\). The trapezoid \(XYCD\) is in the ratio \(p:1\) with the given trapezoid \(ABCD\). Determine \(CY = DX\).

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