
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
The table below shows the sales situation of a certain product in a certain store. The original price of the product is $600$ yuan. With different price reductions (in yuan), the daily sales volume (in units) changes as follows:

| Price Reduction (yuan) | $5$  | $10$ | $15$ | $20$ | $25$ | $30$ | $35$ |
|------------------------|------|------|------|------|------|------|------|
| Daily Sales Volume (units) | $780$ | $810$ | $840$ | $870$ | $900$ | $930$ | $960$ |

$(1)$ What relationship is reflected in the table? Which one is the independent variable and which one is the dependent variable?  
$(2)$ For every $5$ yuan reduction in price, how many units does the daily sales volume increase by? What was the daily sales volume before the price reduction?  
$(3)$ If the selling price is $540$ yuan, what is the daily sales volume?

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