
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
In a class of 48 students, the average score of a test was found to be 70, with a variance of 75. Later, it was discovered that the scores of two students were recorded incorrectly: one student who actually scored 80 was recorded as having 50, and another who scored 70 was recorded as having 100. Calculate the new average score and variance after these corrections.

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