
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 convex quadrilateral \(ABCD\), where \(AB = BC = 15\), \(CD = DA = 20\), and \(\angle D = 60^\circ\). Points \(X\) and \(Y\) are the midpoints of \(\overline{BC}\) and \(\overline{DA}\) respectively. Compute \(XY^2\).

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