
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 $f(x)=(a- \frac {1}{2})e^{2x}+x$ where $a\in\mathbb{R}$.
(I) Find the range of values for the real number $a$ such that $f(x)$ is monotonically increasing in the interval $(-\infty, 0)$.
(II) Find the range of values for $a$ such that the graph of function $f(x)$ is always below the curve $y=2ae^x$ in the interval $(0, +\infty)$.

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