
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
At a distance of \( l \) meters from bridge \( A \) downstream, there is bridge \( B \). When an athlete was swimming past bridge \( A \) towards bridge \( B \), two balls were thrown to him. He caught the first ball and left the second one to float downstream. After swimming a certain distance with the first ball, the athlete left this ball and swam upstream to catch the second ball. After catching the second ball, he turned around and swam towards bridge \( B \), arriving there at the same time as the first ball which was floating freely. What distance did the athlete swim, given that his own speed was always \( k \) times greater than the speed of the current?

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