
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
A large rectangle is tiled by some  $1\times1$  tiles. In the center there is a small rectangle tiled by some white tiles. The small rectangle is surrounded by a red border which is five tiles wide. That red border is surrounded by a white border which is five tiles wide. Finally, the white border is surrounded by a red border which is five tiles wide. The resulting pattern is pictured below. In all,  $2900$  red tiles are used to tile the large rectangle. Find the perimeter of the large rectangle.
[asy]
import graph;
size(5cm);
fill((-5,-5)--(0,-5)--(0,35)--(-5,35)--cycle^^(50,-5)--(55,-5)--(55,35)--(50,35)--cycle,red);
fill((0,30)--(0,35)--(50,35)--(50,30)--cycle^^(0,-5)--(0,0)--(50,0)--(50,-5)--cycle,red);
fill((-15,-15)--(-10,-15)--(-10,45)--(-15,45)--cycle^^(60,-15)--(65,-15)--(65,45)--(60,45)--cycle,red);
fill((-10,40)--(-10,45)--(60,45)--(60,40)--cycle^^(-10,-15)--(-10,-10)--(60,-10)--(60,-15)--cycle,red);
fill((-10,-10)--(-5,-10)--(-5,40)--(-10,40)--cycle^^(55,-10)--(60,-10)--(60,40)--(55,40)--cycle,white);
fill((-5,35)--(-5,40)--(55,40)--(55,35)--cycle^^(-5,-10)--(-5,-5)--(55,-5)--(55,-10)--cycle,white);
for(int i=0;i<16;++i){
draw((-i,-i)--(50+i,-i)--(50+i,30+i)--(-i,30+i)--cycle,linewidth(.5));
}
[/asy]

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