
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 a rectangle measuring $200 \times 300$ meters. There is one guard at each of the four corners of the facility. An intruder approaches the perimeter of the facility from the outside, and all the guards run towards the intruder by the shortest routes along the outer perimeter (while the intruder remains stationary). Three guards cover a total distance 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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