
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
In the rectangular coordinate plane $xOy$, given vectors $\overrightarrow{OA}=(1,5)$, $\overrightarrow{OB}=(7,1)$, $\overrightarrow{OM}=(1,2)$, and point $P$ is a moving point that satisfies $\overrightarrow{OP}=t\overrightarrow{OM}(t\in R)$. Find:
1. The coordinates of vector $\overrightarrow{OP}$ when $\overrightarrow{PA}\cdot\overrightarrow{PB}$ reaches its minimum value.
2. The value of $\cos\angle APB$.

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