
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
Xiao Ming found in a math problem that:

If the complex numbers $z_1=\cos \alpha_1+i\sin \alpha_1$, $z_2=\cos \alpha_2+i\sin \alpha_2$, $z_3=\cos \alpha_3+i\sin \alpha_3$ (where $\alpha_1, \alpha_2, \alpha_3 \in \mathbb{R}$), then $z_1 \cdot z_2=\cos (\alpha_1+\alpha_2)+i\sin (\alpha_1+\alpha_2)$, $z_2 \cdot z_3=\cos (\alpha_2+\alpha_3)+i\sin (\alpha_2+\alpha_3)$. Based on the above conclusions, we can conjecture that $z_1 \cdot z_2 \cdot z_3=$.

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