
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
Let \( a \) be a real number. The equation \(\left(z^{2}-2z+5\right)\left(z^{2}+2az+1\right)=0\) has 4 distinct roots. These roots correspond to 4 points that lie on a circle in the complex plane. Determine the range of values for the real number \( a \).

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