
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) $\int \frac{3x^{2}+8}{x^{3}+4x^{2}+4x} \, dx$
2) $\int \frac{2x^{5}+6x^{3}+1}{x^{4}+3x^{2}} \, dx$
3) $\int \frac{x^{3}+4x^{2}-2x+1}{x^{4}+x} \, dx$
4) $\int \frac{x^{3}-3}{x^{4}+10x^{2}+25} \, dx$

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