
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 \( K_{1} \) notices ship \( K_{2} \), which is at a distance \( d \) from \( K_{1} \) and sailing at a speed \( v \) in a direction perpendicular to the line \( K_{1} K_{2} \). Ship \( K_{1} \) is in need of assistance and wants to get the attention of ship \( K_{2} \), which, however, does not notice \( K_{1} \) and continues on its course. How close can ship \( K_{1} \) get to ship \( K_{2} \) if:

a) the speed of \( K_{1} \) is also \( v \) and the captain of \( K_{1} \) steers directly towards \( K_{2} \) at all times (with the direction of \( K_{2} \) changing continuously as both ships move);

b) the speed of ship \( K_{1} \) is \( u < v \), and the captain of \( K_{1} \) assumes that the direction of \( K_{2} \) will not change, and sets the course of his ship accordingly?

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