
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 triangular racecourse, all runners start at point $A$, must touch the wall which is 1400 meters long, and stop at point $B$. The distance from $A$ to the wall is 500 meters and the distance from $B$ to the wall is 700 meters. Determine the minimum distance a runner must cover in the race, rounding the answer to the nearest meter. The diagram provided below visualizes the setup: 

[asy]
import olympiad; import geometry; size(250);
defaultpen(linewidth(0.8));
draw((0,5)--origin--(14,0)--(14,7));
label("500 m",(0,5)--origin,W); label("1400 m",(0,0)--(14,0),S); label("700 m",(14,0)--(14,7),E);
draw((0,5)--(7,0)--(14,7),linetype("3 3")+linewidth(0.7));
label("$A$",(0,5),N); label("$B$",(14,7),N);
[/asy]

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