
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 reconnaissance plane flies in a circle with center at point $A$. The radius of the circle is $10 \mathrm{kм}$, and the plane's speed is $1000 \mathrm{км/ч}$. At a certain moment, a missile is launched from point $A$, which has the same speed as the plane and is guided such that it always lies on the line connecting the plane with point A. How long after launch will the missile catch up with the plane?

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