
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
Three cyclists ride in the same direction on a circular track with a length of 300 meters. Each of them moves at their own constant speed, and all the speeds are different. A photographer can take a successful picture of the cyclists if they all appear on a segment of the track with a length of \( d \) meters. What is the smallest \( d \) such that the photographer will eventually be able to take a successful picture?

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