
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) Given $a^{ \frac {1}{2}}+a^{- \frac {1}{2}}=3$, find the value of $\frac {a^{2}+a^{-2}+1}{a+a^{-1}-1}$.  
(2) Calculate $\sqrt {(1- \sqrt {2})^{2}}+2^{-2}\times( \frac {9}{16})^{-0.5}+2^{\log_{2}3}-(\lg8+\lg125)$.

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