
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. Huang has 12 grandchildren. Assuming that each grandchild is equally likely to be a boy or a girl independently of the others, what is the probability that Mr. Huang has neither an equal number of grandsons and granddaughters nor all grandchildren being of the same gender?

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