
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 points corresponding to the complex numbers \( z_1, z_2, z_3 \) are \( Z_1, Z_2, Z_3 \), respectively. Given that \(\left| z_1 \right| = \left| z_2 \right| = \sqrt{2}\), \(\overrightarrow{OZ_1} \cdot \overrightarrow{OZ_2} = 0\), and \(\left| z_1 + z_2 - z_3 \right| = 2\), find the range of the value of \(\left| z_3 \right|\).

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