
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 probability of event $A$ occurring in each trial is 1/2. Using Chebyshev's inequality, estimate the probability that the number $X$ of occurrences of event $A$ lies between 40 and 60, if 100 independent trials are conducted.

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