
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
$(1)2\cos 45^{\circ}+\left(3-\pi \right)^{0}-|2-\sqrt{8}|-(-\frac{1}{3})^{-1}$；<br/>$(2)$先化简,再求值:（$\frac{x^{2}-1}{x^{2}-2x+1}-\frac{1}{x-1}$）$÷\frac{x+2}{x-1}$,其中$x=\sqrt{27}+|-2|-3\tan 60^{\circ}$.

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