
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 the hyperbola $\frac {x^{2}}{m} - \frac {y^{2}}{n} = 1$ ($m > 0$, $n > 0$) and the ellipse $\frac {x^{2}}{5} + \frac {y^{2}}{2} = 1$ have the same foci, find the minimum value of $\frac {4}{m} + \frac {1}{n}$.

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