
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
The secret object is a rectangle of $200 \times 300$ meters. Outside the object, each of the four corners has a guard. An intruder approaches the perimeter of the secret object from the outside, and all the guards run towards the intruder by the shortest paths along the outer perimeter (the intruder remains in place). The sum of the distances run by three guards to reach the intruder is 850 meters. 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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