
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 store sells a type of electric fan, with an average daily sales of 24 units and a profit of $60 per unit. In order to increase profits, the store plans to reduce the price appropriately. If the price of each fan is reduced by $5, the average daily sales will increase by 4 units. Let the price reduction per fan be $5x$.

$(1)$ Express the average daily sales volume and profit per unit after the price reduction using algebraic expressions involving $x$.

$(2)$ If the goal is to achieve a daily sales profit of $1540, find the value of $x$.

$(3)$ Can the daily sales profit of the electric fan reach $2000? Please explain the reason.

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