
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 in the Cartesian coordinate plane, points A(-1, 0), B(1, 0), M(4, 0), N(0, 4), and moving points P(x1, y1), Q(x2, y2) satisfy the conditions $\overrightarrow {AP}\cdot \overrightarrow {BP}=1$ and $\overrightarrow {OQ}=( \frac {1}{2}-t) \overrightarrow {OM}+( \frac {1}{2}+t) \overrightarrow {ON}$, where O is the origin, find the minimum value of $| \overrightarrow {QP}|$.

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