
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: $-1^4+\sqrt{(\sqrt{3}-2)^2}+3\tan30°+(-\frac{1}{3})^{-2}-4^{2022} \times 0.25^{2021}$;  
$(2)$ Simplify first and then evaluate: $\frac{a^2-1}{a^2-a}÷(2+\frac{a^2+1}{a})$, where $a$ is the decimal part of $\sqrt{2}$.

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