
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 the value of the expression $(\sqrt {2} +(1)^{2014}+2\cos 45^{\circ}+ \sqrt {16})$.

(2) Simplify and evaluate the expression $\frac {x^{2}+y^{2}-2xy}{x-y}÷( \frac {x}{y}- \frac {y}{x})$, where $x= \sqrt {2}+1$ and $y= \sqrt {2}-1$.

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