
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
Gabriella created a Venn diagram showing the number of students in her physics class who like three different genres of music: Rock, Jazz, and Classical. There are 40 students in her class. Also, she knows $\frac{1}{4}$ of students like Rock, $\frac{1}{5}$ like Jazz, 8 students like other genres (not these three), and 6 students do not like any of these three genres. How many students like all three genres (Rock, Jazz, and Classical)? [asy]unitsize(50);
import graph;
pair A = (0,-1); pair B = (sqrt(3)/2,1/2); pair C = (-sqrt(3)/2,1/2);
draw(Circle(A,1.2) ^^ Circle(B,1.2) ^^ Circle(C,1.2));
label("12",A); label("4",B); label("5",C); label("$z$",(0,0)); label("$w$",(B+C)/2); label("$y$",(A+B)/2); label("$x$",(A+C)/2);
label("Classical",1.5C,C); label("Other Genres",2B,C); label("Rock", 1.7A,A);[/asy]

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