
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 \( ABC \), \( AB = 4 \), \( AC = 5 \), \( BC = 7 \), and \( D \) lies on \( \overline{BC} \) such that \( \overline{AD} \) bisects \( \angle BAC \). Find \( \cos \angle BAD \).

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