
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 vectors $\overrightarrow{m} = (\ln x, 1-a \ln x)$ and $\overrightarrow{n} = (x, f(x))$, where $\overrightarrow{m}$ is parallel to $\overrightarrow{n}$ and $f'(x)$ is the derivative of the function $f(x)$:
(I) If the function $f(x)$ is monotonically decreasing on $(1, +\infty)$, find the minimum value of the real number $a$;
(II) If there exist $x_1, x_2 \in [e, e^2]$ such that $f(x_1) \leq f'(x_2) + a$, find the range of values for the real number $a$.

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