
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 shows the miles traveled by cyclists Carlos and Diana. After three hours, how many more miles has Carlos cycled than Diana? [asy]
/* Adapted AMC8-like problem */
draw((0,0)--(5,0)--(5,3.75)--(0,3.75)--cycle);
for(int x=0; x <= 5; ++x) {
for(real y=0; y <=3.75; y+=0.75) {
dot((x, y));
}
}
draw((0,0)--(3,2.25));  // Diana's line
draw((0,0)--(3,3));  // Carlos' line
label(rotate(37.5)*"Diana", (1.5,1.1));
label(rotate(45)*"Carlos", (1.5,1.5));
label(scale(0.75)*rotate(90)*"MILES", (-1, 2));
label(scale(0.75)*"HOURS", (2.5, -1));

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);
[/asy]

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