
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
Given $x=3+2\sqrt{2}$ and $y=3-2\sqrt{2}$, find:<br/>$(1)$ $x+y=$______；$x-y=$______；$xy=\_\_\_\_\_\_.$<br/>$(2)$ Calculate the value of the expression $x^{2}-3xy+y^{2}-x-y$.

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