
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
At an open evening at the conservatory, four quartets, five duets, and six trios were supposed to perform (a quartet consists of four musicians, a trio consists of three, and a duet consists of two; each musician is only part of one musical group). However, one quartet and two duets unexpectedly went on tour, and the soloist of one of the trios fell ill, and the members of this trio had to perform as a duo. How many musicians performed at the conservatory that evening?

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