
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 $\overrightarrow{O P}=(2,1)$, $\overrightarrow{O A}=(1,7)$, and $\overrightarrow{O B}=(5,1)$, let $C$ be a point on the line $O P$ (where $O$ is the origin). Find the coordinates of $\overrightarrow{O C}$ when $\overrightarrow{C A} \cdot \overrightarrow{C B}$ takes its minimum value.

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