
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 or simplify: $2\cos45^\circ-\left(-2\sqrt {3}\right)^0+\frac{1}{\sqrt {2}+1}- \sqrt {8}$
(2) Simplify first, then evaluate: $\left(\frac{3}{x-1}-x-1\right)\div\frac{x-2}{x^{2}-2x+1}$, where $x=-\sqrt {2}$;

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