
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: $\sqrt{2}\sin45{}°-(-\frac{1}{2})^{-2}-(-1)^{2023}$;<br/>$(2)$ Simplify first, then evaluate: $(\frac{x+2}{x}-\frac{x-1}{x-2})÷\frac{x-4}{x^2-4x+4}-1$, where $x$ is the square root of $4$.

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