
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 field is shaped as a trapezoid with parallel sides measuring 150 meters and 250 meters, respectively, and the non-parallel sides each measuring 200 meters. The angles adjacent to the longer base are 120 degrees each. At harvest, the crop at any point in the field is brought to the nearest point on the field's perimeter. Determine the fraction of the crop that is brought to the longest side.

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