
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 kite-shaped field planted uniformly with wheat. The field is defined with vertices A, B, C, and D such that AB = BC = 100 m, and AD = DC = 150 m. Angle A and C are 90 degrees each. The wheat at any point in the field is harvested and brought to the nearest point on the perimeter of the field. Calculate the fraction of the crop that is taken to one of the diagonals (BD).

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