
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 length of an interval $[x\_1, x\_2]$ is defined as $|x\_2 - x\_1|$, the domain and range of the function $f(x) = \frac{(m^2 + m)x - 1}{m^2x} (m \in \mathbb{R}, m \neq 0)$ are both $[a, b]$. Determine the maximum length of the interval $[a, b]$.

A) $\frac{2\sqrt{3}}{3}$
B) $\frac{\sqrt{3}}{3}$
C) $\sqrt{3}$
D) $3$

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