
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
Wei Long spicy strips are a brand of popular snacks on the market, especially among students. A convenience store on Jianxue Street wholesales a portion of this snack for sale. It is known that the cost price of each pack of Wei Long spicy strips is twice the cost price of each pack of regular spicy strips. It is found that buying Wei Long spicy strips for $40$ yuan gets $10$ more packs than buying regular spicy strips for $10$ yuan.<br/>$(1)$ Find the cost price of each pack of Wei Long spicy strips and regular spicy strips, respectively, in yuan.<br/>$(2)$ The convenience store spends $1000$ yuan per month to purchase Wei Long spicy strips and regular spicy strips, and sells them all at prices of $3.5$ yuan per pack and $2$ yuan per pack, respectively. If the quantity of regular spicy strips does not exceed three times the quantity of Wei Long spicy strips, help the convenience store design a purchasing plan to maximize the total profit obtained each month.

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