
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 king and queen had three sons and some daughters (at least one). On September 1st of a certain year, the king and queen noticed that they were both 35 years old, and moreover, the total age of their children was also 35 years. Several years later, on September 1st, the king and queen noticed that their combined age was equal to the total age of all their children. (During this time, no new children were born, and no members of the family passed away.)

How many children does the royal couple have if it is known that they have no more than 20? List all possible options.

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