
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
Given Chloe is $2$ years older than Joey, and Zoe is $1$ year old, and there are $7$ distinct birthdays, including today, on which Joey's age will be an integral multiple of Zoe's age, determine the sum of the two digits of Chloe's age the next time her age is a multiple of Zoe's age.

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