
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
Simplify and evaluate  
(1) Simplify $$\frac {x-1}{x^{ \frac {2}{3}}+x^{ \frac {1}{3}}+1}+ \frac {x+1}{x^{ \frac {1}{3}}+1}- \frac {x-x^{ \frac {1}{3}}}{x^{ \frac {1}{3}}-1}$$;  
(2) If $2\lg(3x-2)=\lg x+\lg(3x+2)$, find the value of $$\log_{ \sqrt {x}} \sqrt {2 \sqrt {2 \sqrt {2}}}$$.

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