
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
The vector \( \overline{OA} \) forms angles with the axes \( Ox \), \( Oy \), and \( Oz \) equal to \( \alpha=\frac{\pi}{3} \), \( \beta=\frac{\pi}{3} \), and \( \gamma=\frac{\pi}{4} \) respectively. The point \( B \) has coordinates \((-2, -2, -2 \sqrt{2})\). Find the angle between the vectors \( \overline{OA} \) and \( \overline{OB} \).

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