
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 field where wheat has been uniformly planted. The vertices of the trapezoid are labeled \(A\), \(B\), \(C\), and \(D\) in sequence, with \(AB\) parallel to \(CD\) and the lengths given as \(AB = 150 \text{ m}\) and \(CD = 200 \text{ m}\). \(AB\) is inclined at \(70^\circ\) to the perpendicular dropped from \(B\) to side \(CD\), and \( \angle BCD = 135^\circ\). At harvest, the wheat at any point in the field is collected and brought to the closest point on the field's perimeter. Determine the fraction of the harvest that is brought to the longest side.

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