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

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