
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: $(\frac{1}{2})^{-2} - (\pi - 3)^{0} + |\sqrt{3} - 2| + 2\sin 60^{\circ}$; $(2)$ Simplify first, then evaluate: $(\frac{{x+1}}{{x-2}} - 1) \div \frac{{x^2 - 2x}}{{x^2 - 4x + 4}}$, where the integer $x$ forms the three sides of $\triangle ABC$ with $2$ and $3$. Find the values of all algebraic expressions that satisfy the conditions.

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