
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
Calculate the average student headcount for the spring and fall terms of the academic years `05-`06 and `06-`07. Due to a report error for the fall term of `06-`07, you can use this approximate headcount as 11000 students.

[asy]
unitsize(0.35 cm);

fill((15,0)--(15,11.2)--(18,11.2)--(18,0)--cycle,gray(.5));
fill((18,0)--(18,11.1)--(21,11.1)--(21,0)--cycle,gray(.7));

fill((22,0)--(22,10.8)--(25,10.8)--(25,0)--cycle,gray(.5));
fill((25,0)--(25,11)--(28,11)--(28,0)--cycle,gray(.7));

draw((0,0)--(0,15)--(30,15)--(30,0)--cycle,linewidth(1));
label("11,200",(16.5,12), fontsize(10));
label("11,100",(19.5,11.5), fontsize(10));

label("10,800",(23.5,11.5), fontsize(10));
label("11,000~",(26.5,12), fontsize(10));
label("Student Headcount (2005-2006 to 2007-2008)",(15,17));
label("'05-'06",(18,0),S);
label("'06-'07",(25,0),S);
label("Academic Year",(15,-2),S);

fill((32,11)--(32,9)--(34,9)--(34,11)--cycle,gray(.5));
fill((32,8)--(32,6)--(34,6)--(34,8)--cycle,gray(.7));
label("Fall ",(34,10),E, fontsize(10));
label("Spring ",(34,7),E, fontsize(10));

[/asy]

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