
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
Below is a histogram showing the number of home runs hit in May for the top hitters in the league. Calculate the mean number of home runs hit by these players for this month.

[asy]
draw((24,0)--(0,0)--(0,18));
label("5",(3,-1)); // 5 home runs minimal category
label("6",(6,-1));
label("7",(9,-1));
label("9",(12,-1));
label("10",(15,-1)); // 10 home runs maximum category
// Representation of players for each home run category
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((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((12,.5)..(12.5,1)..(12,1.5)..(11.5,1)..cycle);
fill((15,.5)..(15.5,1)..(15,1.5)..(14.5,1)..cycle);
fill((15,2)..(15.5,2.5)..(15,3)..(14.5,2.5)..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}
user