
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 parachutes into a completely random point in a perfectly square forest with dimensions $10 \times 10$ km. Upon landing, he immediately starts broadcasting important information to the enemy.

At each of the four corners of the forest, there are radio direction finders, each capable of detecting the transmitter's signal at a distance of up to 10 km. For the counterintelligence to accurately determine the coordinates of the active transmitter, the signal must be detected by at least two of these direction finders.

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

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