
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
Compute $Z_1 = i^4 + i^5 + i^6 + \ldots + i^{12}$ and $Z_2 = i^4 \cdot i^5 \cdot i^6 \cdot \ldots \cdot i^{12}$, and find the relationship between $Z_1$ and $Z_2$.

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