
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
Mr. Greene has 8 children, including one set of twins who are of the same gender. Assuming that for the other 6 children, the gender of each is determined independently with equal likelihood of male and female, calculate the probability that Mr. Greene has more sons than daughters or more daughters than sons.

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