
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 earns a profit of $60$ yuan per unit, with an average daily sales of $40$ units. In order to reduce inventory, the store has decided to take appropriate price reduction measures. After investigation, it was found that for every $1$ yuan reduction in price per unit, the store can sell an additional $2$ units per day.  
$(1)$ When the profit per unit decreases to $50$ yuan, how many units can be sold per day?  
$(2)$ By how much should the price per unit be reduced for the store to achieve a daily profit of $3000$ yuan?  
$(3)$ Can the daily profit of the store reach $3300$ yuan? Please explain the reason.

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