
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 the following expressions:

(1) Simplify the expression $\frac{x-1}{x^{\frac{2}{3}}+x^{\frac{1}{3}}+1} + \frac{x+1}{x^{\frac{1}{3}}+1} - \frac{x-x^{\frac{1}{3}}}{x^{\frac{1}{3}}-1}$;

(2) If $2\log(3x-2) = \log x + \log(3x+2)$, 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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