
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 $\overrightarrow{OP} = (2, 1)$, $\overrightarrow{OA} = (1, 7)$, $\overrightarrow{OB} = (5, 1)$, and let $C$ be a point on line $OP$ (where $O$ is the origin of the coordinate),
(1) Find $\overrightarrow{OC}$ when $\overrightarrow{CA} \cdot \overrightarrow{CB}$ reaches its minimum value;
(2) Based on the point $C$ found in (1), calculate $\cos \angle ACB$.

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