
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 planar vectors $\overrightarrow {OA}=(1,7)$, $\overrightarrow {OB}=(5,1)$, and $\overrightarrow {OP}=(2,1)$:
(Ⅰ) If the vector $k\overrightarrow {OA} + 2\overrightarrow {OB}$ is parallel to $2\overrightarrow {OA} - \overrightarrow {OB}$, find the value of the real number $k$.
(Ⅱ) If point $Q$ is a moving point on line $OP$, find the minimum value of $\overrightarrow {QA} \cdot \overrightarrow {QB}$.

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