
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
Someone, not carefully reading the previous problem, asked Dr. Sharadek how to determine the course based on the given conditions. Unfortunately, they forgot which of the ships has the higher speed and which has the lower speed, but remembered that the ratio of the speeds $k$ is known and is less than 1. However, they did not know whether $k$ represents the ratio of the signaling ship's speed to the spotted ship's speed or vice versa. Yet, the master immediately determined the course based on the incomplete data. How did Dr. Sharadek achieve this?

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