
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
If  $\min \left \{ \frac{ax^2+b}{\sqrt{x^2+1}} \mid x \in \mathbb{R}\right \} = 3$ , then (1) Find the range of  $b$ ; (2) for every given  $b$ , find  $a$ .

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