
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
Let \( m \) and \( a \) be the number of elementary school students and their average height, respectively, and let \( n \) and \( b \) be the number of students in other grades and their average height. Then the average height of the students in the school is \(\frac{a m + b n}{m+n}\).

Given: 
\[ a = \alpha b, \quad \alpha = \left(1 - \frac{25}{100}\right) = \frac{3}{4} \]
\[ a = \beta \frac{a m + b n}{m+n}, \quad \beta = \left(1 - \frac{15}{100}\right) = \frac{19}{20} \]

Therefore, 
\[ \alpha b = \beta \frac{\alpha b m + b n}{m+n} \]
\[ \rightarrow \frac{m}{n} = \frac{\beta - \alpha}{\alpha \beta - \alpha} = \frac{8}{9} \approx 0.89 \]

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