
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 $a=\frac{\sqrt{5}+1}{2}$ and $b=\frac{\sqrt{5}-1}{2}$, find the values of the following expressions:  
$(1) \frac{b}{a}+\frac{a}{b}$  
$(2) a^{2}+b^{2}+ab$.

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