
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 the vectors $\overrightarrow{OA}=(-1,-3)$, $\overrightarrow{OB}=(5,3)$, $\overrightarrow{OM}=(2,2)$ in the plane, and point $P$ lies on the line $OM$ such that $\overrightarrow{PA}\cdot \overrightarrow{PB}=-16$.
1. Find the coordinates of $\overrightarrow{OP}$.
2. Find the cosine value of $\angle APB$.
3. For $t\in R$, find the minimum value of $|\overrightarrow{OA}+t\overrightarrow{OP}|$.

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