
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
Given the function $f(x)=x^{2}+b\ln (x+1)$, where $b\neq 0$.
(1) If $b=-12$, find the minimum value of $f(x)$ on $[1,3]$;
(2) If $f(x)$ has both a maximum and a minimum value in its domain, find the range of real number $b$.

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