
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 frequency histogram below represents the number of school days missed by Ms. Johnson's 20 students. Calculate by how many days the mean number of days missed per student is greater than the median number of days missed per student. Express your answer as a common fraction.

[asy]
draw((0,0)--(0,6),linewidth(2));
draw((0,0)--(8,0),linewidth(2));

draw((0,0)--(1,0)--(1,2)--(0,2)--(0,0)--cycle,linewidth(2));
draw((1,0)--(2,0)--(2,5)--(1,5)--(1,0)--cycle,linewidth(2));
draw((2,0)--(3,0)--(3,1)--(2,1)--(2,0)--cycle,linewidth(2));
draw((3,0)--(4,0)--(4,3)--(3,3)--(3,0)--cycle,linewidth(2));
draw((4,0)--(5,0)--(5,2)--(4,2)--(4,0)--cycle,linewidth(2));
draw((5,0)--(6,0)--(6,4)--(5,4)--(5,0)--cycle,linewidth(2));
draw((6,0)--(7,0)--(7,1)--(6,1)--(6,0)--cycle,linewidth(2));
draw((7,0)--(8,0)--(8,2)--(7,2)--(7,0)--cycle,linewidth(2));

draw((0,1)--(8,1),dashed);
draw((0,2)--(8,2),dashed);
draw((0,3)--(8,3),dashed);
draw((0,4)--(8,4),dashed);
draw((0,5)--(8,5),dashed);

label("0",(0.5,0),S);
label("1",(1.5,0),S);
label("2",(2.5,0),S);
label("3",(3.5,0),S);
label("4",(4.5,0),S);
label("5",(5.5,0),S);
label("6",(6.5,0),S);
label("7",(7.5,0),S);

label("1",(0,1),W);
label("2",(0,2),W);
label("3",(0,3),W);
label("4",(0,4),W);
label("5",(0,5),W);

label("Number of School Days Missed",(4,8));
label("by Ms. Johnson's Students",(4,7));

label("$\#$ of Days of School Missed",(4,-2));

label(rotate(90)*"$\#$ of Students",(-2,3));
[/asy]

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