
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\\).

(Ⅰ) Find \\(a\\);

(Ⅱ) Determine the intervals of monotonicity for the function \\(f(x)\\);

(Ⅲ) 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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