
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 derivative.

$$
y=\frac{1}{12} \cdot \ln \frac{x^{4}-x^{2}+1}{\left(x^{2}+1\right)^{2}}-\frac{1}{2 \sqrt{3}} \operatorname{arctg} \frac{\sqrt{3}}{2 x^{2}-1}
$$

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