
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
Convex quadrilateral  $ABCD$  with perpendicular diagonals satisfies  $\angle B = \angle C = 90^\circ$ ,  $BC=20$ , and  $AD=30$ . Compute the square of the area of a triangle with side lengths equal to  $CD$ ,  $DA$ , and  $AB$ .


*2021 CCA Math Bonanza Tiebreaker Round #2*

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