
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, each participant starts at point $A$, must touch any part of the 1200-meter wall, and finish at point $B$. The vertical distance from $A$ to the bottom of the wall is 300 meters, and from $B$ to the top of the wall is 600 meters. Calculate the minimum distance a runner must cover, rounding off to the nearest meter. Assume a flat terrain.
[asy]
import olympiad; import geometry; size(250);
defaultpen(linewidth(0.8));
draw((0,3)--origin--(12,0)--(12,6));
label("300 m",(0,3)--origin,W); label("1200 m",(0,0)--(12,0),S); label("600 m",(12,0)--(12,6),E);
draw((0,3)--(6,0)--(12,6),linetype("3 3")+linewidth(0.7));
label("$A$",(0,3),N); label("$B$",(12,6),N);
[/asy]

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