
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
Two chords \( PQ \) and \( PR \) are drawn in a circle with diameter \( PS \). The point \( T \) lies on \( PR \) and \( QT \) is perpendicular to \( PR \). The angle \(\angle QPR = 60^\circ\), \( PQ = 24 \text{ cm} \), and \( RT = 3 \text{ cm} \). What is the length of the chord \( QS \) in cm?

A) \( \sqrt{3} \)  
B) 2  
C) 3  
D) \( 2\sqrt{3} \)  
E) \( 3\sqrt{2} \)

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