
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
$(1)$ Simplify: $\sqrt{8}-|1-\sqrt{2}|+2^{-2}-2\sin 45^{\circ}$; <br/>$(2)$ Simplify first, then evaluate: $\left(\frac{x^2-2}{x-2}-x\right) \div \frac{x-1}{x^2-4x+4}$, where $x=-\frac{1}{2}$.

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