
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 the Ivanov family, which has many children but no twins, a reporter came to interview them. During the interview, each of the children said, "I have an older brother." After thinking about it, the reporter was very surprised. But the father explained that some of the children were joking, and only six of them were telling the truth. How many children can there be in this family, given that there are 4 more boys than girls? List all possible options.

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