
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
Calculation Questions  
(1) $\int_{1}^{2} \left( \frac{1}{\sqrt{x}} + \frac{1}{x} + \frac{1}{x^2} \right) dx$  
(2) $\frac{-2\sqrt{3} + i}{1 + i2\sqrt{3}} + \left( \frac{\sqrt{2}}{1 + i} \right)^{2000} + \frac{1 + i}{3 - i}$.

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