
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 park shaped like a kite is displayed as follows: Vertices are labeled A at the top, B and D at the bottom left and right respectively, and C at the bottom center forming a kite shape with AC and BC as diagonals intersecting at right angles. AB and DC are congruent, as are AD and BC. The angles at B and D are 120°, and at A and C are 60°. AB and BC are each 100 meters. Determine the fraction of the park from which any waste or litter is brought to the longest diagonal for disposal, where disposal sites are located at the ends of each line segment.

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