
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 company's sales department provides information on the sales revenue $(y_{1}$ yuan), sales cost $(y_{2}$ yuan), and sales volume $(x$ tons) of a certain product as follows:<br/>①When $x=0$, $y_{2}=2000$;<br/>②When $x=2$, $y_{1}=2000$, $y_{2}=3000$;<br/>③$y$ is directly proportional to $x$;<br/>④$y$ is a linear function of $x$.<br/>Based on the above information, solve the following problems:<br/>$(1)$ Find the functional relationships of $y_{1}$, $y_{2}$, and $x$ respectively;<br/>$(2)$ For how many tons of sales volume are the sales revenue and sales cost the same?<br/>$(3)$ When the sales volume is 10 tons, find the sales profit. (Profit $=$ Sales revenue $-$ Sales cost)

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