
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
In a race, all runners start at point $A$, must touch any part of a 1600-meter long wall, and then stop at point $B$. The wall is placed horizontally between $A$ and $B$. The distance from $A$ to the closest point on the wall is 600 meters vertically, and from the wall to $B$ is 800 meters vertically. Determine the minimum distance a participant must run, rounding to the nearest meter. Assume the race takes place on a flat plane.

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