
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 $\overset{→}{OA}=(1,7), \overset{→}{OB}=(5,1), \overset{→}{OP}=(2,1)$, and point $Q$ is a moving point on line $OP$.

(1) Find the coordinates of $\overset{→}{OQ}$ when $\overset{→}{QA} \cdot \overset{→}{QB}$ reaches its minimum value;

(2) When point $Q$ satisfies the conditions and conclusions of (1), find the value of $\cos ∠AQB$.

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