
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: $\sqrt{3}\tan 45^{\circ}-\left(2023-\pi \right)^{0}+|2\sqrt{3}-2|+(\frac{1}{4})^{-1}-\sqrt{27}$; <br/>$(2)$ Simplify first, then evaluate: $\frac{{{x^2}-x}}{{{x^2}+2x+1}}\div (\frac{2}{{x+1}}-\frac{1}{x})$, simplify it first, then choose an integer you like as the value of $x$ within the range of $-2 \lt x \lt 3$ to substitute and evaluate.

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