
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
Given $x+y=6$ and $xy=5$, find the values of the following expressions:  
$(1) \frac {2}{x}+ \frac {2}{y}$  
$(2) (x-y)^{2}$  
$(3) x^{2}+y^{2}$．

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