
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
Calculate the value of the following expressions:  
(1) $0.001^{- \frac {1}{3}} - \left(\frac {7}{8}\right)^0 + 16^{ \frac {3}{4}} + \left(\sqrt {2} \cdot 33 \right)^6$  
(2) $\frac {2\lg2+\lg3}{1+ \frac {1}{2}\lg0.36+ \frac {1}{4}\lg16}$  
(3) Given $x^{ \frac {1}{2}}+x^{- \frac {1}{2}}=3$, find the value of $x+x^{-1}$.

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