
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
Eating zongzi during the Dragon Boat Festival is a traditional custom of the Chinese nation. The wholesale price of pork zongzi is $10$ yuan more expensive per box than the wholesale price of red bean zongzi. The wholesale price of one box of pork zongzi plus two boxes of red bean zongzi is $100$ yuan.  
$(1)$ Find the wholesale price of each box of pork zongzi and red bean zongzi.  
$(2)$ In sales, a merchant found that when the selling price of each box of pork zongzi is $50$ yuan, 100 boxes can be sold per day. If the selling price per box is increased by $1$, then 2 fewer boxes are sold per day. Let the selling price of each box of pork zongzi be $a$ yuan, and the profit from selling pork zongzi be $w$ yuan. Find the maximum profit the merchant can make per day from selling pork zongzi.

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