
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
$(1)$ Calculate:<br/>① $\sqrt{9}-\sqrt{{{({-2})}^2}}$;<br/>② $|{\sqrt{2}-\sqrt{3}}|-({\sqrt{\frac{1}{4}}+\sqrt[3]{{-27}}})$;<br/>$(2)$ Find the value of $x$ in the following expressions:<br/>① $4x^{2}-15=1$;<br/>② $\left(x+1\right)^{3}+64=0$.

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