
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 A and B are moving points on the circle $$C_{1}: x^{2} + y^{2} = 1$$, and $$AB = \sqrt{3}$$, P is a moving point on the circle $$C_{2}: (x-3)^{2} + (y-4)^{2} = 1$$. The range of values for $$|\overrightarrow{PA} + \overrightarrow{PB}|$$ is \_\_\_\_\_\_.

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