
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 with a radio transmitter descends by parachute into a random point within a perfectly square forest of $10 \times 10$ km. Upon landing, he immediately starts transmitting important information to the enemy.

There are radio direction-finders located at each of the four corners of the forest, each capable of detecting the transmitter within a 10 km radius. In order for counterintelligence to accurately determine the coordinates of the transmitting spy, at least two direction-finders need to detect the transmitter.

The spy is lucky: one of the direction-finders is not operational today. What is the probability that the counterintelligence will not be able to determine the coordinates of the spy's landing location?

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