
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 diagram portrays the miles traveled by cyclists Carmen and Daniel. After six hours, approximately how many more miles has Carmen cycled than Daniel? [asy]
/* Modified AMC8 1999 #4 Problem */
draw((0,0)--(7,0)--(7,5.25)--(0,5.25)--cycle);
for(int x=0; x <= 7; ++x) {

for(real y=0; y <=5.25; y+=0.75)

{

dot((x, y));

}
}
draw((0,0)--(6,4.5));
draw((0,0)--(6,3.75));
label(rotate(30)*"Daniel", (3.6,1.5));
label(rotate(37.5)*"Carmen", (3.5,3));
label(scale(0.75)*rotate(90)*"MILES", (-1, 2.75));
label(scale(0.75)*"HOURS", (3.5, -1));

label(scale(0.85)*"105", (0, 5.25), W);
label(scale(0.85)*"90", (0, 4.5), W);
label(scale(0.85)*"75", (0, 3.75), W);
label(scale(0.85)*"60", (0, 3), W);
label(scale(0.85)*"45", (0, 2.25), W);
label(scale(0.85)*"30", (0, 1.5), W);
label(scale(0.85)*"15", (0, 0.75), W);
label(scale(0.86)*"1", (1, 0), S);
label(scale(0.86)*"2", (2, 0), S);
label(scale(0.86)*"3", (3, 0), S);
label(scale(0.86)*"4", (4, 0), S);
label(scale(0.86)*"5", (5, 0), S);
label(scale(0.86)*"6", (6, 0), S);
label(scale(0.86)*"7", (7, 0), S);
[/asy]

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