
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 $f(x) = a\ln(1+x) + x^2 - 10x$  
(1) If $x=3$ is an extremum point of the function, find the monotonic intervals of $f(x)$.  
(2) If $f(x)$ is a decreasing function on the interval $[1, 4]$, find the range of values for $a$.

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