
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
There were 15 different non-integer numbers written on a board. For each number \( x \) among these fifteen, Vasya wrote down separately \( [x] \) and \( \frac{1}{\{x\}} \). What is the minimum number of distinct numbers that could appear in Vasya's notebook?

(Note: \( [x] \) and \( \{x\} \) represent the integer and fractional parts of the number \( x \), respectively.)

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