
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 that $x=3$ is an extreme value point of the function $f(x)=a\ln (1+x)+x^{2}-10x$.
(1) Find the value of $a$;
(2) Find the monotonic intervals of the function $f(x)$;
(3) If the line $y=b$ intersects the graph of the function $y=f(x)$ at 3 points, find the range of $b$.

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