
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
The distance \( AB \) is 100 km. Cyclists depart simultaneously from \( A \) and \( B \) towards each other with speeds of 20 km/h and 30 km/h respectively. Along with the first cyclist from \( A \), a fly departs with a speed of 50 km/h. The fly travels until it meets the cyclist from \( B \), then turns around and flies back to meet the cyclist from \( A \), and continues this pattern. How many kilometers will the fly travel in the direction from \( A \) to \( B \) before the cyclists meet?

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