
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 $F$ is the right focus of the hyperbola $C$: $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ ($a > 0, b > 0$), $A$ and $B$ are respectively the left and right vertices of $C$. $O$ is the origin, $D$ is a point on $C$, and $DF \perp x$-axis. A line through point $A$ intersects segment $DF$ at point $E$ and intersects the $y$-axis at point $M$. The line $BE$ intersects the $y$-axis at point $N$. If $3|DM| = 2|ON|$, then the eccentricity of the hyperbola $C$ is ______.

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