
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
Two transformations are applied to the complex number $-4 - 6i$:

1. A $60^\circ$ rotation around the origin in the counter-clockwise direction.
2. A dilation, centered at the origin, with scale factor $\sqrt{2}$.
3. Finally, a translation by the vector $2 + 2i$.

What is the resulting complex number?

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