
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 \( A \) and \( B \) be the endpoints of a semicircular arc with a radius of \( 4 \). The arc is divided into five equal parts by four points \( D_1, D_2, D_3, D_4 \). All chords of the form \( \overline{AD_i} \) or \( \overline{BD_i} \) 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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