
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
In a certain middle school, the number of eighth-grade students is greater than the number of seventh-grade students. One day during the radio exercises (with no absences from either seventh or eighth grade students), the eighth-grade students formed a rectangular array with each row consisting of $(3a+b)$ students and there were $\left(2a+2b\right)$ rows. The seventh-grade students formed a square array with $2\left(a+b\right)$ rows and $2\left(a+b\right)$ students in each row, where $a > b$.  
$(1)$ Find the difference in the number of students between the eighth grade and the seventh grade at this school (expressed in terms of $a$ and $b$).  
$(2)$ When $a=10$ and $b=2$, find the difference in the number of students between the eighth grade and the seventh grade at this school.

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