
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
Calculate the corrected average score and variance of a class of 50 students, given that the original average was 70 and the original variance was 102, after two students' scores were corrected from 50 to 80 and from 90 to 60.

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