
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
What music do you like the best? Perhaps theme music from anime? Or maybe you like gaming theme music from YouTubing gamers on arcade games!**p11.** Every note in a musical phrase that is  $2$  measures long lasts for  $1/8$  of the measure of  $1/4$  of it. How many different rhythms can the phrase have if there are no rests?**p12.** I play a random chord of three different notes. It is called dissonant if the distance between any two of those notes are  $1$ ,  $2$ ,  $6$ ,  $10$ , or  $11$  semitones apart. Given that the longest distance between two notes is at most  $12$  semitones, what is the probability that the chord will be dissonant?**p13.** Two distinct notes are called an interval and if they are  $0, 5$ , or  $7$  semitones apart modulo  $12$ , they are a perfect interval. (Modulo  $12$  means the remainder when divided by  $12$ .) If a piano has  $88$  notes, and consecutive notes are  $1$  semitone apart, how many perfect intervals can be played?**p14.** An ensemble has a violin, a viola, and a cello. A chord has 3 notes and each instrument can play  $1$  or  $2$  of them at a time. How many ways can they play the chord if every note in the chord must be played? (Octaves don’t matter.)


PS. You should use hide for answers.

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