
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 the plane vectors $\overset{→}{m}$ and $\overset{→}{n}$ is $\dfrac{π}{6}$, and $|\overset{→}{m}| = \sqrt{3}$, $|\overset{→}{n}| =2$, in $\triangle ABC$, $\overset{→}{AB}=2 \overset{→}{m}+2 \overset{→}{n}$, $\overset{→}{AC}=2 \overset{→}{m}-6 \overset{→}{n}$, and $D$ is the midpoint of $BC$, calculate the magnitude of $\overset{→}{AD}$.

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