
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 the complex numbers \( z_1 \) and \( z_2 \) satisfy \( \left|z_1\right| < 1 \), \( \left|z_2\right| < 1 \), \( z_1 + z_2 \) is real, and \( z_1 + z_2 + z_1 z_2 = 0 \), find the range of values of \( z_1 z_2 \).

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