
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 an ellipse $\frac {x^{2}}{3m^{2}} + \frac {y^{2}}{5n^{2}} = 1$ and a hyperbola $\frac {x^{2}}{2m^{2}} - \frac {y^{2}}{3n^{2}} = 1$ share a common focus.  
(1) Find the equation of the asymptotes of the hyperbola;  
(2) Line $l$ passes through the right focus and is perpendicular to the x-axis. If the area of the triangle formed by line $l$ and the asymptotes of the hyperbola is $\frac { \sqrt {3}}{4}$, find the equation of the hyperbola.

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