
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 focus of the parabola $x^2=2my$ ($m>0$) is $F$, and its directrix intersects with the hyperbola $\frac{x^2}{m^2} - \frac{y^2}{n^2} = 1$ ($n>0$) at two points $A$ and $B$. If $\angle AFB = 120^\circ$, then the eccentricity of the hyperbola is ______.

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