
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
A certain high school in Shandong province has set up two clubs with local characteristics, "Clay Sculpture" and "Paper Cutting," to meet the development requirements of students. It is known that a total of 800 students have signed up for these two clubs. According to the requirements, each person can only participate in one club. The number of students from each grade participating in the clubs is as follows:

| Club     | Grade 10 | Grade 11 | Grade 12 |
|----------|----------|----------|----------|
| Clay Sculpture | $a$ | $b$ | $c$ |
| Paper Cutting  | $x$ | $y$ | $z$ |

Given that $x:y:z=5:3:2$, and the number of students in the "Clay Sculpture" club accounts for $\frac{3}{5}$ of the total number of students in both clubs. In order to understand the satisfaction level of students in both clubs, a sample of 50 students is selected for a survey. How many students should be selected from the Grade 11 "Paper Cutting" club?

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