
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 trapezoid field is uniformly planted with wheat. The trapezoid has one pair of parallel sides measuring 80 m and 160 m, respectively, with the longer side on the bottom. The other two non-parallel sides each measure 120 m. The angle between a slanted side and the longer base is $45^\circ$. At harvest, the wheat at any point in the field is brought to the nearest point on the field's perimeter. What fraction of the crop is brought to the longest side?

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