
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/>$(1)9\sqrt{3}-7\sqrt{12}+5\sqrt{48}$;<br/>$(2)(\sqrt{\frac{5}{3}}-\sqrt{15})\times \sqrt{3}$;<br/>$(3)\frac{\sqrt{75}-\sqrt{12}}{\sqrt{3}}$;<br/>$(4)(3+\sqrt{5})(3-\sqrt{5})-(\sqrt{3}-1)^{2}$;<br/>$(5)$Given $x_{1}=\frac{2}{\sqrt{5}+\sqrt{3}}$, $x_{2}=\sqrt{5}+\sqrt{3}$, find the value of ${x}_{1}^{2}+{x}_{2}^{2}$.

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