
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 $\overrightarrow{OP} = (2,1)$, $\overrightarrow{OA} = (1,7)$, $\overrightarrow{OB} = (5,1)$, let C be a point on the line OP (where O is the origin of coordinates),
(1) Find $\overrightarrow{OC}$ such that $\overrightarrow{CA} \cdot \overrightarrow{CB}$ has the 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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