
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
During the recent "National Day" holiday, a supermarket prepared for the shopping peak during the holiday by selling two brands of laundry detergent, brand A and brand B. The cost price of brand A laundry detergent is $10 less per bottle compared to brand B laundry detergent. The supermarket purchased the same number of bottles of brand A laundry detergent for $3000 and brand B laundry detergent for $4000.<br/>$(1)$ Find the cost prices of brand A and brand B laundry detergents;<br/>$(2)$ For sales, the supermarket decided to sell brand A laundry detergent for $45 per bottle, selling 100 bottles per day. However, it was found that when the selling price of brand B laundry detergent is $50 per bottle, 140 bottles can be sold per day. Furthermore, for every $1 increase in the selling price of brand B laundry detergent, 2 fewer bottles are sold per day. What selling price per bottle of brand B laundry detergent will result in a total daily profit of $4700 when combined with brand A laundry detergent?

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