
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
Solve the systems of equations:

First system:
\[
\left\{
\begin{array}{l}
z_{1}+2 z_{2}=1+i \\
3 z_{1}+i z_{2}=2-3 i 
\end{array}
\right.
\]

Second system:
\[
\left\{
\begin{array}{l}
|z+1-i|=|z+i| \\
|3+2 i-z|=|z+i|
\end{array}
\right.
\]

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