
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. Outside the facility, at each of the four corners, there is a guard. An intruder approached the perimeter of the secret facility, and all the guards ran towards the intruder along the shortest paths on the external perimeter (the intruder stayed in place). Three guards ran a combined 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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