
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
A certain product can be sold at an average of $60$ units per day, with a profit of $100$ yuan per unit. In order to reduce inventory quickly, the store decides to take appropriate price reduction measures. After investigation, it is found that for each unit of product, for every $1$ yuan reduction in price, the store can sell an additional $2$ units per day. Based on this rule, please answer:<br/>$(1)$ When the store sells $80$ units per day, how much profit does the store make per day?<br/>$(2)$ By how much should the price of each unit be reduced for the store to make a daily profit of $8400$ yuan?

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