
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
The complex numbers \( z_1, z_2, \cdots, z_{100} \) satisfy: \( z_1 = 3 + 2i \), \( z_{n+1} = \overline{z_n} \cdot i^n \) for \( n = 1, 2, \cdots, 99 \) (where \( i \) is the imaginary unit). Find the value of \( z_{99} + z_{100} \).

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