
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
If the moving point \\(P\\) is on line \\(a\\): \\(x-2y-2=0\\), and the moving point \\(Q\\) is on line \\(b\\): \\(x-2y-6=0\\), and the midpoint of segment \\(PQ\\) is denoted as \\(M(x_{0},y_{0})\\), and \\((x_{0}-2)^{2}+(y_{0}+1)^{2} \leqslant 5\\), then the range of values for \\(x_{0}^{2}+y_{0}^{2}\\) is \_\_\_\_\_\_.

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