
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 \(\vec{O}P = (2,1)\), \(\vec{O}A = (1,7)\), and \(\vec{O}B = (5,1)\), let \(X\) be a point on the line \(OP\) (with \(O\) as the coordinate origin). Find the measure of the angle \(\angle AXB\) when the dot product \(\vec{X}A \cdot \vec{X}B\) is minimized.

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