
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
Let $\min \frac{x-1}{x^{2}+1}=a$ and $\max \frac{x-1}{x^{2}+1}=b$. What are the minimum and maximum of the functions:

a) $\frac{x^{3}-1}{x^{6}+1}$ 

b) $\frac{x+1}{x^{2}+1}$?

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