
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
For guarding an offshore oil platform, it is necessary to place 5 radars around it, each having a coverage area with a radius of $r=13$ km. Determine the maximum distance from the center of the platform at which they need to be placed to ensure coverage of the platform by a ring of radars with a width of 10 km. Calculate the area of this coverage ring.

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