
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
Let \( T \) be a trapezoid with two right angles and side lengths \( 4, 4, 5 \), and \( \sqrt{17} \). Two line segments are drawn, connecting the midpoints of opposite sides of \( T \) and dividing \( T \) into 4 regions. If the difference between the areas of the largest and smallest of these regions is \( d \), compute \( 240d \).

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