
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: $27^{ \frac {2}{3}} - 2^{log_{4}3} \times log_{2} \frac {1}{8} + log_{2}3 \times log_{3}4$;  
(2) Given $0 < x < 1$, and $x + x^{-1} = 3$, find the value of $x^{ \frac {1}{2}} - x^{- \frac {1}{2}}$.

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