
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 the following:
1. $(-\frac{1}{2})^{-2}+(\pi -3.14)^{0}+|\sqrt{3}-2|+\frac{\sqrt{6}×\sqrt{3}}{\sqrt{2}}$;
2. $(3\sqrt{12}-2\sqrt{\frac{1}{3}}-\sqrt{48})÷4\sqrt{3}-(\sqrt{2}-1)^{0}$;
3. Solve the equation: $(2x-1)^{2}-27=0$;
4. Solve the equation: $\frac{(x+1)^2}{3}-4=0$.

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