
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
If there exist real constants $k$ and $b$, such that the functions $f(x)$ and $G(x)$ satisfy $F(x) \geq kx + b$ and $G(x) \leq kx + b$ for any real number $x$ in their common domain, then the line $y = kx + b$ is called the "isolating line" of $f(x)$ and $G(x)$. Given the functions $f(x) = x^2$ ($x \in \mathbb{R}$), $g(x) = \frac{1}{x}$ ($x < 0$), $h(x) = 2e\ln x$ (where $e$ is the base of the natural logarithm), the following propositions are made:
1. $m(x) = f(x) - g(x)$ is monotonically increasing for $x \in \left(-\frac{1}{{\sqrt[3]{2}}}, 0\right)$;
2. There exists an "isolating line" between $f(x)$ and $g(x)$, and the minimum value of $b$ is $-4$;
3. There exists an "isolating line" between $f(x)$ and $g(x)$, and the range of $k$ is $\left[-4, 1\right]$;
4. There exists a unique "isolating line" between $f(x)$ and $h(x)$, $y = 2\sqrt{e}x - e$.

Identify the number of the true proposition.

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