
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 the line $OP$.

1. Find $|\overrightarrow {OA}+\overrightarrow {OB}|$.
2. When $\overrightarrow {QA}\cdot \overrightarrow {QB}$ reaches its minimum value, find the coordinates of $\overrightarrow {OQ}$.

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