
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 a function $f(x) = a\ln(1+x) + x^2 - 10x$ where the tangent line at the point $(2, f(2))$ is perpendicular to the line $3x - 2y - 1 = 0$.  
(1) Find the value of the real number $a$;  
(2) Determine the intervals of monotonicity for the function $f(x)$;  
(3) If the line $y=b$ intersects the graph of $y=f(x)$ at three points, find the range of values for $b$.

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