
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 $z = \frac{-2+6i}{1-i} - 4$.
(1) Find the conjugate of the complex number $z$.
(2) If $w = z + ai$, where $a$ is a real number, and $|w| \leq |z|$, find the range of values for $a$.

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