
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
Steve has an isosceles triangle with a base of 12 inches and a height of 10 inches. He intends to divide this triangle into twelve pieces that have equal areas. To the nearest hundredth of an inch, what is the number of inches in the greatest perimeter among the twelve pieces?
[asy]
size(150);
defaultpen(linewidth(0.7));
draw((0,0)--(12,0));
for(int i = 0; i < 13; ++i){
draw((6,10)--(i,0));
}
draw((0,-0.5)--(12,-0.5),Bars(5));
label("$12''$",(0,-0.5)--(12,-0.5),S);
[/asy]

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