
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 brand of toys is purchased at a unit price of $30$ yuan. According to market research, when the selling price is $40$ yuan, the sales volume is 600 units. Furthermore, for every increase of $1$ yuan in the selling price, 10 fewer toys are sold.
$(1)$ Let the selling price of this brand of toys be $x$ yuan $(x > 40)$. Write down the functional relationship between the sales volume $y$ and $x$ directly.
$(2)$ Under the conditions in (1), if the store earns a sales profit of $10,000$ yuan, what should be the selling price $x$ of the toy?
$(3)$ Under the conditions in (1), if the toy factory stipulates that the selling price of this brand of toys should not be less than $44$ yuan, and the store needs to complete a sales task of at least 540 units, what is the maximum profit that the store can earn from selling this brand of toys?

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