
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 plane vectors $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$ satisfying $|\overrightarrow{a}| = |\overrightarrow{b}| = \sqrt{5}$, $|\overrightarrow{c}| = 1$, if $(\overrightarrow{a} - \overrightarrow{c}) \cdot (\overrightarrow{b} - \overrightarrow{c}) = 0$, determine the range of $|\overrightarrow{a} - \overrightarrow{b}|$.

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