
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
The domain of functions $f(x)$ and $g(x)$ is $D$, and the line $x=x_0$ ($x_0 \in D$) intersects the graphs of $y=f(x)$ and $y=g(x)$ at points $A$ and $B$ respectively. If the value of $|AB|$ is a non-zero constant, then the curves $y=f(x)$ and $y=g(x)$ are called "parallel curves". Given $f(x)=e^x-\ln x+c$ ($a>0$, $c \neq 0$), and $y=f(x)$, $y=g(x)$ are "parallel curves" on the interval $(0, +\infty)$, $g(1)=e$, and $g(x)$ has a unique zero point in the interval $(2,3)$, then the range of values for $a$ is \_\_\_\_\_\_.

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