
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 extremum point of the function $f(x)=a\ln(1+x)+x^2-10x$.

(1) Find $a$;  
(2) Determine the intervals of monotonicity for the function $f(x)$;  
(3) If the line $y=b$ intersects the graph of the function $y=f(x)$ at three points, find the range of values for $b$.

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