
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
Suppose there exists a complex number $z$ that simultaneously satisfies the following conditions:
1. The point corresponding to the complex number $z$ in the complex plane is located in the second quadrant.
2. $z \cdot \overline{z} + 2iz = 8 + ai (a \in \mathbb{R})$. Find the range of values for $a$.

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