
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 object is a rectangle measuring $200 \times 300$ meters. Outside the object, there is one guard stationed at each of the four corners. An intruder approached the perimeter of the secret object from the outside, and all the guards ran towards them via the shortest paths along the external perimeter (the intruder remained stationary). Three guards ran 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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