
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 $P$ is a moving point on the ellipse $\dfrac{x^{2}}{16} + \dfrac{y^{2}}{12} = 1$, and $M$, $N$ are two points on the circle $(x-2)^{2} + y^{2} = 1$ with $MN = \sqrt{3}$, then the range of values for $|\overrightarrow{PM} + \overrightarrow{PN}|$ is \_\_\_\_\_\_.

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