
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 the minimum value of the function $f(x) = x^2 - a \ln x (a > 0)$ is $1$.
(I) Find the value of $a$;
(II) If the equation $f^2(x)e^x - 6m f(x) + 9m e^{-x} = 0$ has a unique real root in the interval $[1, +\infty)$, find the range of values for $m$.

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