
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
The field shown has been planted uniformly with corn. It forms a trapezoid where two non-parallel sides meet at a vertex with an angle of $60^\circ$, and the opposite vertex has an angle of $120^\circ$. Each side of the trapezoid measures $150$ m, $150$ m, $200$ m, and $200$ m respectively, starting from one of the $60^\circ$ angles and moving clockwise. At harvest, the corn at any point in the field is brought to the nearest point on the field's perimeter. What is the fraction of the crop that is brought to the longest side?

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