
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
Simplify first, then find the value:  
$(1) x(\sqrt{6}-x)+(x+\sqrt{5})(x-\sqrt{5})$, where $x=\sqrt{6}-\sqrt{2}$;  
$(2)$ Let $a=\sqrt{3}+\sqrt{2}$, $b=\sqrt{3}-\sqrt{2}$. Find $a-b$ and the value of $a^{2}-2ab+b^{2}$.

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