
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 recent years, the consumption of pre-made meals has been on the rise, satisfying consumers' needs and expanding the development of the food industry. A certain catering platform plans to launch two types of pre-made meals, $A$ and $B$. It is known that selling $1$ portion of meal $A$ and $2$ portions of meal $B$ yields a profit of $35$ yuan, while selling $2$ portions of meal $A$ and $3$ portions of meal $B$ yields a profit of $60$ yuan.  
$(1)$ Find the profit for each portion of meal $A$ and $B$.  
$(2)$ Based on the sales situation, the catering platform can sell a total of $1000$ portions of meals $A$ and $B each day, with the quantity of meal $A$ not exceeding $\frac{3}{2}$ times the quantity of meal $B$. How should they purchase the meals to maximize the total profit? What is the maximum profit?

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