
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
Ship \( O_{1} \) spots another ship, \( O_{2} \), which at the moment of observation is moving perpendicular to the line \( O_{1} O_{2} \). Ship \( O_{2} \) does not notice the signals from \( O_{1} \) and maintains its initial course and speed \( v_{2} \). Ship \( O_{1} \) wants to attract attention because it needs help, and sails at its maximum possible speed \( v_{1} \) in such a direction as to get as close as possible to \( O_{2} \). What course should it take? What will be the distance between the two ships at the moment of their closest approach if the initial distance was \( d \) and the ratio of their speeds \( v_{1} / v_{2} \) is \( k \) and less than 1?

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