
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

Recently, the following game has become popular: \( A \) tells \( B \): "Write down your shoe size (as an integer!), add 9 to it. Multiply the resulting number by 2, and then add 5. Multiply the resulting sum by 50, and add 1708. Subtract your birth year from this sum. Tell me the result!" \( B \), who has been silently calculating, answers: 4720. \( A \)'s response: "Your shoe size is 38, and you are 14 years old!" \( A \) does the same with \( C \), but asks to add 7 instead of 9 to the shoe size, and to increase the 50-times product by 1711 instead of 1708. \( C \)'s result is 5059. What is \( C \)'s shoe size and age? Moreover, what is the explanation of this game?

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