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

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