
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
To implement labor education, a certain school invited experts from the Agricultural Science Institute to guide students in planting cherry tomatoes. After experiments, the average yield per plant $y$ in kilograms is related to the number of plants planted per square meter $x$ (where $2\leqslant x\leqslant 8$, and $x$ is an integer). When planting 2 plants per square meter, the average yield per plant is 4 kilograms. Under the same cultivation conditions, for each additional plant per square meter, the yield per plant decreases by 0.5 kilograms.  
$(1)$ Find the function expression of $y$ in terms of $x$.  
$(2)$ How many plants should be planted per square meter to obtain the maximum yield? What is the maximum yield in kilograms?

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