
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 1978, a person introduced their family by saying: "I have one son and one daughter, and they are not twins. The cube of my son's age plus the square of my daughter's age equals the year of my birth. I was born after 1900. Both of my children are under 21 years old. I am 8 years older than my wife." Find the ages of each family member in 1978.

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