
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
A rectangle ABCD has sides AB = 30, BC = 40, CD = 30, and DA = 40. Diagonals AC and BD intersect at point O. Check if triangles formed by these segments are right triangles and subsequently if the diagonals of the rectangle are equal. Determine the area of triangle AOB.
A) 300 sq units
B) 375 sq units
C) 450 sq units
D) 525 sq units

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