
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
A spy-plane circles point A at a distance of 10 km with a speed of 1000 km/h. A missile is fired towards the plane from point A at the same speed and moves so that it is always on the line between point A and the plane. How long does it take for the missile to hit the plane?

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