
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 functions $f(x)=ax-\ln x$ and $F(x)=e^{x}+ax$, where $x > 0$, $a < 0$, and $e$ is the base of the natural logarithm.
(I) Find the range of values for the real number $a$ such that $f(x)$ and $F(x)$ have the same monotonicity in the interval $(0,\ln 3)$.
(II) If $a\in(-\infty,-\frac{1}{e^{2}}]$, and the minimum value of the function $g(x)=xe^{ax-1}-2ax+f(x)$ is $M$, find the minimum value of $M$.

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