
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 convex quadrilateral $ABCD$, $AB = BC = 15$, $CD = DA = 20$, and $\angle C = 90^\circ$. Points $X$ and $Y$ are the midpoints of $\overline{AB}$ and $\overline{CD}$ respectively. Compute $XY^2$ (the square of the length of $XY$).

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