
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
Let $a$ be a real number, and let the complex numbers $z_1=a-2i$ and $z_2=-1+ai$. If $z_1+z_2$ is a pure imaginary number, then find the value of $z_1z_2$.

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