
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
The ratio of the number of students in the strong math foundation groups of schools A, B, and C in the Huzhou area is $3:2:1$. There are a total of 48 students in the strong math foundation programs in the three schools. In a unified exam, the average score of all students is 117, with a variance of 21.5. It is known that the average scores of the strong math foundation groups in schools A and B are 118 and 114, with variances of 15 and 21, respectively. Find the variance of the students' scores in school C.

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