
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
A regular dodecagon $Q_1 Q_2 \dotsb Q_{12}$ is drawn in the coordinate plane with $Q_1$ at $(1,0)$ and $Q_7$ at $(-1,0)$. If $Q_n$ is the point $(x_n, y_n)$, compute the numerical value of the product \[(x_1 + y_1 i)(x_2 + y_2 i)(x_3 + y_3 i) \dotsm (x_{12} + y_{12} i).\]

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