
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 pentagon is drawn in the coordinate plane with one vertex at $(2,0)$ and its center at $(4,0)$. If $Q_n$ is the point $(x_n, y_n)$, compute the numerical value of the product
\[(x_1 + y_1 i)(x_2 + y_2 i)(x_3 + y_3 i)(x_4 + y_4 i)(x_5 + y_5 i).\]

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