
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 grade holds a science and technology festival, with two venues, $A$ and $B$, where each student can only go to one venue. $25\%$ of the students go to venue $A$, and the rest go to venue $B$. The distribution of students from each grade in venues $A$ and $B$ is shown in the table below:

|        | Grade 10 | Grade 11 | Grade 12 |
|--------|----------|----------|----------|
| Venue $A$ | $50\%$   | $40\%$   | $10\%$   |
| Venue $B$ | $40\%$   | $50\%$   | $10\%$   |

Let $x$, $y$, and $z$ represent the proportions of students in grades 10, 11, and 12, respectively, out of the total number of students in the school. Using stratified random sampling, a sample of size $n$ is drawn from all students participating in the event.
- Find the ratio of $x:y:z$.
- If there are 75 students from grade 11 at venue $B$, determine the value of $n$ and the number of students from grades 10, 11, and 12 at venue $A$.

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