
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 total number of students who participated in the math test at the school is 1000 and the test scores are approximately normally distributed with a mean of 100 and a variance of $\sigma^2$. If the probability that a student's score falls within the interval $[80, 100]$ is 0.45, estimate the number of students with scores above 120.

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