
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
In $\triangle ABC$, $\angle BAC = 60^\circ$. The angle bisector of $\angle BAC$, line segment $AD$, intersects $BC$ at $D$ and satisfies $\overrightarrow{AD} = \frac{1}{4} \overrightarrow{AC} + t \overrightarrow{AB}$. Given that $AB = 8$, find the length of $AD$.

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