
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 hexagon $P_1 P_2 \dotsb P_6$ is drawn in the coordinate plane with $P_1$ at $(1,0)$ and $P_4$ at $(1,3).$ If $P_n$ is the point $(x_n,y_n),$ compute the numeric value of the product
\[(x_1 + y_1 i)(x_2 + y_2 i)(x_3 + y_3 i)\dotsm(x_6 + y_6 i).\]

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