
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 $\overrightarrow{OA} = (1, 7)$, $\overrightarrow{OB} = (5, 1)$, $\overrightarrow{OP} = (2, 1)$, and point Q is a moving point on line OP.
(I) When $\overrightarrow{QA} \perp \overrightarrow{OP}$, find the coordinates of $\overrightarrow{OQ}$;
(II) When $\overrightarrow{OA} \cdot \overrightarrow{QB}$ takes the minimum value, find the coordinates of $\overrightarrow{OQ}$.

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