
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 that \(\overrightarrow{O P}=(2,1), \overrightarrow{O A}=(1,7), \overrightarrow{O B}=(5,1)\), and where \(X\) is a point on the line \(O P\), determine the angle \(\angle A X B\) when \(\vec{X} \vec{A} \cdot \overrightarrow{X B}\) takes its minimum value.

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