
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
Find all complex numbers $z$ that simultaneously satisfy the following two conditions:
1) $z + \frac{10}{z}$ is a real number, and $1 < z + \frac{10}{z} \leqslant 6$;
2) The real and imaginary parts of $z$ are both integers.

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