
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 10 units of type $A$ and 20 units of type $B$ computers, making a profit of 4000 yuan. Selling 20 units of type $A$ and 10 units of type $B$ computers yields a profit of 3500 yuan. <br/>$(1)$ Find the profit from selling each unit of type $A$ and type $B$ computers. <br/>$(2)$ The store plans to purchase a total of 100 computers of both types. Let $x$ be the number of type $A$ computers purchased. The total profit from selling these 100 computers is $y$ yuan. Find the functional relationship of $y$ with respect to $x$. <br/>$(3)$ Under the conditions of question $(2)$, if at least 20 units of type $A$ computers are purchased, what is the profit from purchasing 100 computers of both types?

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