
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 point $O$ is the coordinate origin, $P$ and $Q$ are moving points on the circle $x^{2}+y^{2}=4$, and $\angle POQ=\dfrac{2\pi }{3}$. Point $M$ is moving on the line $3x+4y-12=0$. Find the minimum value of $| \overset{}{{MP}}+\overset{}{{MQ}} |$.

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