
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 \( P \) spots ship \( Q \), which is moving in a direction perpendicular to \( PQ \), maintaining its course. Ship \( P \) chases \( Q \), always heading directly towards \( Q \); the speed of both ships at any moment is the same (but can change over time). It is clear without calculations that \( P \) travels along a curved path; if the chase lasts long enough, the trajectory of the pursuing ship and the trajectory of the fleeing ship eventually become nearly identical. What will the distance \( PQ \) be then, if initially it was 10 nautical miles?

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