
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
Mila and Zhenya each thought of a number and wrote down all the natural divisors of their numbers on the board. Mila wrote 10 numbers, Zhenya 9 numbers, and the number 6 appeared twice. How many distinct numbers are on the board in total?

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