
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
Let $P$ and $Q$ be the endpoints of a semicircular arc of radius $3$. The arc is divided into five congruent arcs by four equally spaced points $D_1$, $D_2$, $D_3$, $D_4$. All chords of the form $\overline {PD_i}$ or $\overline {QD_i}$ are drawn. Find the product of the lengths of these eight chords.

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