
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
Eight students participate in a pie-eating contest. The graph shows the number of pies eaten by each participating student. Sarah ate the most pies and Tom ate the fewest. Calculate how many more pies than Tom did Sarah eat and find the average number of pies eaten by all the students.

[asy]
defaultpen(linewidth(1pt)+fontsize(10pt));
pair[] yaxis = new pair[10];
for( int i = 0 ; i < 10 ; ++i ){

yaxis[i] = (0,i);

draw(yaxis[i]--yaxis[i]+(17,0));
}
draw((0,0)--(0,9));
draw((17,9)--(17,0));

fill((1,0)--(1,3)--(2,3)--(2,0)--cycle,grey);
fill((3,0)--(3,4)--(4,4)--(4,0)--cycle,grey);
fill((5,0)--(5,8)--(6,8)--(6,0)--cycle,grey);
fill((7,0)--(7,5)--(8,5)--(8,0)--cycle,grey);
fill((9,0)--(9,7)--(10,7)--(10,0)--cycle,grey);
fill((11,0)--(11,6)--(12,6)--(12,0)--cycle,grey);
fill((13,0)--(13,2)--(14,2)--(14,0)--cycle,grey);
fill((15,0)--(15,1)--(16,1)--(16,0)--cycle,grey);
label("0",yaxis[0],W);
label("1",yaxis[1],W);
label("2",yaxis[2],W);
label("3",yaxis[3],W);
label("4",yaxis[4],W);
label("5",yaxis[5],W);
label("6",yaxis[6],W);
label("7",yaxis[7],W);
label("8",yaxis[8],W);
label("9",yaxis[9],W);
label("Students/Participants",(8.5,0),S);
label("Results of a Pie-Eating Contest",(8.5,9),N);
label(rotate(90)*"$\#$ of Pies Eaten",(-1,4.5),W);
[/asy]

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