
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 vectors $\overrightarrow {m}$ and $\overrightarrow {n}$ satisfy $\overrightarrow {m} = (2,0)$ and $\overrightarrow {n} = \left( \frac {3}{2}, \frac { \sqrt {3}}{2} \right)$. For triangle $ABC$, $\overrightarrow {AB} = 2\overrightarrow {m} + 2\overrightarrow {n}$ and $\overrightarrow {AC} = 2\overrightarrow {m} - 6\overrightarrow {n}$. Find the magnitude of $\overrightarrow {AD}$.

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