
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
On the Dragon Boat Festival, Supermarket A is having a promotion on apples. The price of apples is $10$ yuan per kilogram. If you buy more than $4$ kilograms of apples at once, the part exceeding $4$ kilograms is sold at a discount of $40\%$. Let $x$ (unit: kg) represent the weight of apples purchased, and $y$ (unit: yuan) represent the amount paid.
$(1)$ Buying $3.5$ kilograms of apples at Supermarket A requires ______ yuan, and buying $6$ kilograms of apples requires ______ yuan.
$(2)$ Find the analytical expression of the function $y_A$ representing the amount paid for buying apples at Supermarket A in terms of the purchase weight $x$.
$(3)$ On the same day of the Dragon Boat Festival, the neighboring Supermarket B is also having a promotion on apples. The price of the same apples at Supermarket B is $8$ yuan per kilogram. Wenwen wants to buy $m$ kilograms of apples and finds it more cost-effective to buy at Supermarket B than at Supermarket A. Find the range of values for $m$.

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