
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
Find the integrals:
1) $\int \frac{d x}{\sqrt{x}+\sqrt[4]{x}}$
2) $\int \frac{x+\sqrt{1+x}}{\sqrt[3]{1+x}} d x$
3) $\int \frac{\sqrt{x}}{x^{2} \sqrt{x-1}} d x$

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