
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 vectors \(\overrightarrow{OP} = (2,1)\), \(\overrightarrow{OA} = (1,7)\), and \(\overrightarrow{OB} = (5,1)\), let \(C\) be a point on the line \(OP\) (with \(O\) as the origin). When the dot product \(\overrightarrow{CA} \cdot \overrightarrow{CB}\) reaches its minimum value, find the coordinates of \(\overrightarrow{OC}\).

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