
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
The equilateral triangle \(PQR\) has side length 1. The lines \(PT\) and \(PU\) trisect the angle \(RPQ\), the lines \(RS\) and \(RT\) trisect the angle \(QRP\), and the lines \(QS\) and \(QU\) trisect the angle \(PQR\). What is the side length of the equilateral triangle \(STU\)?

A) \(\frac{\cos 80^{\circ}}{\cos 20^{\circ}}\)

B) \(\frac{1}{3} \cos 20^{\circ}\)

C) \(\cos ^{2} 20^{\circ}\)

D) \(\frac{1}{6}\)

E) \(\cos 20^{\circ} \cos 80^{\circ}\)

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