
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 a square \(ABCD\) with side length \(4 \sqrt{2}\). Point \(O\) is chosen in the plane of the square such that \(OB = 10\) and \(OD = 6\).

Find the angle between the vector \(\overrightarrow{OB}\) and the vector directed from point \(O\) to the vertex of the square furthest from it.

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