
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
Define a new sequence of complex numbers by \( z_1 = 1 \) and
\[ z_{n + 1} = z_n^2 \cdot (1+i) \]
for all \( n \ge 1 \). In the complex plane, find the distance of \( z_5 \) from the origin.

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