
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 that $z_1 = \frac {\sqrt {3}}{2}a + (a+1)i$ and $z_2 = -3\sqrt {3}b + (b+2)i$ where $a, b \in \mathbb{R}$. If $z_1 - z_2 = 4\sqrt {3}$, find $a+b$.

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