
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 chart below describes the number of home runs hit in June by the top hitters in the league. Calculate the mean (average) number of home runs hit by these players.

[asy]
draw((18,0)--(0,0)--(0,18));
label("5",(3,-1));
label("9",(6,-1));
label("7",(9,-1));
label("11",(12,-1));
fill((3,.5)..(3.5,1)..(3,1.5)..(2.5,1)..cycle);
fill((3,2)..(3.5,2.5)..(3,3)..(2.5,2.5)..cycle);
fill((3,3.5)..(3.5,4)..(3,4.5)..(2.5,4)..cycle);
fill((3,5)..(3.5,5.5)..(3,6)..(2.5,5.5)..cycle);
fill((3,6.5)..(3.5,7)..(3,7.5)..(2.5,7)..cycle);
fill((6,.5)..(6.5,1)..(6,1.5)..(5.5,1)..cycle;
fill((6,2)..(6.5,2.5)..(6,3)..(5.5,2.5)..cycle);
fill((6,3.5)..(6.5,4)..(6,4.5)..(5.5,4)..cycle);
fill((9,.5)..(9.5,1)..(9,1.5)..(8.5,1)..cycle);
fill((9,2)..(9.5,2.5)..(9,3)..(8.5,2.5)..cycle);
fill((9,3.5)..(9.5,4)..(9,4.5)..(8.5,4)..cycle;
fill((9,5)..(9.5,5.5)..(9,6)..(8.5,5.5)..cycle);
fill((12,.5)..(12.5,1)..(12,1.5)..(11.5,1)..cycle);
fill((12,2)..(12.5,2.5)..(12,3)..(11.5,2.5)..cycle);
label("Number of Home Runs",(9,-3));
picture perpLabel;
label(perpLabel,"Number of Top Hitters");
add(rotate(90)*perpLabel,(-1,9));
[/asy]

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