
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
Consider a trapezoid in a field planted uniformly with potatoes. The side lengths and angles are modified so that one pair of adjacent angles are \(45^\circ\) and \(135^\circ\), ensuring one pair of opposite sides are parallel. The lengths of the non-parallel sides are \(100 \text{ m}\) and the small base is \(80 \text{ m}\). The longer base is unknown, but it's longer than \(100 \text{ m}\). At harvest, all the potatoes are transported to the nearest point on the field's perimeter. Determine the fraction of the crop that is transported to the longest side.

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