
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 a complex number $z$ that satisfies the following two conditions:
① The real and imaginary parts of $z$ are both integers, and the corresponding point in the complex plane is located in the fourth quadrant.
② $1 < z+ \frac{2}{z} \leq 4$
(I) Find the complex number $z$;
(II) Calculate $| \overline{z} + \frac{2-i}{2+i} |$.

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