
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
Given a class of 48 students with an initial average score of 70 and a variance of 75, and given that the scores of two students were recorded incorrectly (one scored 80 instead of 50 and the other scored 70 instead of 100), calculate the correct average and variance after the corrections.

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