
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 that the angle between vectors $\overrightarrow{m}$ and $\overrightarrow{n}$ is $\frac{\pi}{6}$, and that $|\overrightarrow{m}| = \sqrt{3}$, $|\overrightarrow{n}| = 2$, in triangle $ABC$, $\overrightarrow{AB} = \overrightarrow{m} + \overrightarrow{n}, \overrightarrow{AC} = \overrightarrow{m} - 3\overrightarrow{n}$. If $D$ is the midpoint of side $BC$, find the magnitude of $\overrightarrow{AD}$.

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