
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
Regular dodecagon \( Q_1 Q_2 \ldots Q_{12} \) 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
\[
(x_1 + y_1 i)(x_2 + y_2 i)(x_3 + y_3 i) \ldots (x_{12} + y_{12} i).
\]

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