
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
Every 12 minutes, Bus A completes a trip from \( P \) to \( X \) to \( S \) to \( X \) to \( P \). Every 20 minutes, Bus B completes a trip from \( Q \) to \( X \) to \( T \) to \( X \) to \( Q \). Every 28 minutes, Bus C completes a trip from \( R \) to \( X \) to \( U \) to \( X \) to \( R \). Determine the number of times between 5:00 p.m. and 10:00 p.m. that two or more buses will arrive at \( X \) at the same time.

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