
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 rules for a race require that all runners start at $A$, touch any part of the 1500-meter wall, and stop at $B$. What is the number of meters in the minimum distance a participant must run? Express your answer to the nearest meter. The triangle formed by $A$, $B$, and the nearest point on the wall directly below $A$ has side lengths of 400 meters and 600 meters, respectively.
[asy]
import olympiad; import geometry; size(250);
defaultpen(linewidth(0.8));
draw((0,4)--origin--(15,0)--(15,6));
label("400 m",(0,4)--origin,W); label("1500 m",(0,0)--(15,0),S); label("600 m",(15,0)--(15,6),E);
draw((0,4)--(7.5,0)--(15,6),linetype("3 3")+linewidth(0.7));
label("$A$",(0,4),N); label("$B$",(15,6),N);
[/asy]

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