
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
Fill the natural numbers \(1 \sim 22\) in the boxes below (each box can hold only one number). Among the 11 fractions formed, the maximum number of fractions with integer values is \(\qquad\).

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