
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 \\(f(x)=ax+x\ln x(a\in \mathbb{R})\\).

    \\((I)\\) The slope of the tangent line to the curve \\(y=f(x)\\) at the point \\((1,f(1))\\) is \\(0\\). Find the intervals of monotonicity for \\(f(x)\\);

\\((II)\\) If \\(f(x) < x^{2}\\) holds true for all \\((1,+\infty )\\), find the range of values for \\(a\\).

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