
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

Two cyclists depart simultaneously from point \( A \) with different speeds and travel to point \( B \). Upon reaching \( B \), they immediately turn back. The first cyclist, who is faster than the second, meets the second cyclist on the return journey at a distance of \( a \) km from \( B \). Then, after reaching \( A \), the first cyclist travels again towards \( B \), and after covering \(\boldsymbol{k}\)-th part of the distance \( AB \), meets the second cyclist, who is returning from \( B \). Find the distance from \( \boldsymbol{A} \) to \( \boldsymbol{B} \).

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