
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
In the complex plane, the corresponding points of the complex numbers \( z_1, z_2, z_3 \) are \( Z_1, Z_2, Z_3 \) respectively. Given that:
\[ \left|z_1\right| = \left|z_2\right| = \sqrt{2}, \overrightarrow{O Z_1} \cdot \overrightarrow{O Z_2} = 0, \text{ and } \left|z_1 + z_2 - z_3\right| = 2, \]

find the range of values for \( \left|z_3\right| \).

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