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

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