
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 secret facility is in the shape of a rectangle measuring $200 \times 300$ meters. There is a guard at each of the four corners outside the facility. An intruder approached the perimeter of the secret facility from the outside, and all the guards ran towards the intruder by the shortest paths along the external perimeter (while the intruder remained in place). Three guards ran a total of 850 meters to reach the intruder. How many meters did the fourth guard run to reach the intruder?

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