
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 complex numbers $z_{1}=1+2i$, $z_{2}=-2+i$, $z_{3}=-\sqrt{3}-\sqrt{2}i$, $z_{4}=\sqrt{3}-\sqrt{2}i$, and the corresponding points of $z_{1}$, $z_{2}$, $z_{3}$, $z_{4}$ in the complex plane are $A$, $B$, $C$, $D$ respectively, then $\angle ABC+\angle ADC=$____.

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