
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 the complex number $z$ that satisfies $z=(-1+3i)(1-i)-4$.
(1) Find the conjugate of the complex number $z$;
(2) If $\omega=z+ai$, and the modulus of the vector corresponding to the complex number $\omega$ is not greater than the modulus of the vector corresponding to the complex number $z$, find the range of values for the real number $a$.

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