
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
Define $f(M) = (m, n, p)$, where $M$ is a point inside $\triangle ABC$, and $m$, $n$, $p$ are respectively the areas of $\triangle MBC$, $\triangle MCA$, $\triangle MAB$. Given in $\triangle ABC$, $\overrightarrow {AB} \cdot \overrightarrow {AC} = 2 \sqrt {3}$, $\angle BAC = 30^\circ$, $f(N) = \left( \frac {1}{2}, x, y \right)$, find the minimum value of $\frac {1}{x} + \frac {4}{y}$.

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