
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
$(1)$ Find the value of: ${({2\frac{7}{9}})^{0.5}}+{0.1^{-2}}+{({2\frac{{10}}{{27}}})^{-\frac{2}{3}}}-3{π^0}+\frac{{37}}{{48}}$;<br/>$(2)$ Given that $a$ and $b$ are the two roots of the equation $x^{2}-6x+4=0$, and $a \gt b \gt 0$, find the value of $\frac{{\sqrt{a}-\sqrt{b}}}{{\sqrt{a}+\sqrt{b}}}$.

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