
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
Doctor and his guest Sherlock Holmes were sitting by an open window. Cheerful voices of a large group of children were heard from the garden.

Guest: Please tell me, how many children do you have?

Host: It's not just mine, but children from four families. My group is the largest, my brother's group is smaller, my sister's group is even smaller, and the uncle's group is the smallest. They make such a random noise because there are not enough of them to form two teams of 9 each. Curiously, if you multiply the number of children from the four families, you get the number of our house, which you know.

Guest: I attended a school of mathematics. I will try to calculate the number of children in each of your families.

After some calculations the guest stated: "There is not enough data to solve the problem. Tell me, did the uncle have one child or more?" The host gave the required answer, but we do not know its content.

Guest: Now I can give an exact answer about the number of children.

Question: What was the number of the house and how many children are there in each of the four families?

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