
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
Calculate:<br/>$(1)(\sqrt{7}-\sqrt{13})(\sqrt{7}+\sqrt{13})+(\sqrt{3}+1)^{2}-\frac{\sqrt{6}×\sqrt{3}}{\sqrt{2}}+|-\sqrt{3}|$;<br/>$(2)$ Given:$a \lt 0$, simplify $\sqrt{4-{{({a+\frac{1}{a}})}^2}}-\sqrt{4+{{({a-\frac{1}{a}})}^2}}$.

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