
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
(I) If $t \in R$, $t \neq 0$, find the range of the modulus of the complex number $z = \frac{1}{t} + ti$.
(II) Solve the equation $|z|^{2} + (z + \overline{z})i = \frac{3-i}{2+i}$ in the complex number field ($i$ is the imaginary unit).

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