
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 $z$ satisfying $z=\frac{-2+6i}{1-i}-4$.  
(I) Find the conjugate of the complex number $\overline{z}$.  
(II) If $\omega =z+ai$ and $|\omega| \leqslant |z|$, find the range of the real number $a$.

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