
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)=x{{e}^{x}}+a{{x}^{2}}-x\\), where \\(a∈R\\).

\\((I)\\) When \\(a=-\frac{1}{2}\\), find the intervals of monotonicity for the function \\(f(x)\\).

\\((II)\\) If for \\(x \geqslant 0\\), it always holds that \\(f'(x)-f(x) \geqslant (4a+1)x\\), find the range of the real number \\(a\\).

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