
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
Laura drew five circles, inside which she wants to place positive integers in such a way that they form an equality between a fraction and its integer value.

How many ways can Laura place the numbers 2, 3, 5, 6, and 11 inside the five circles to make the equality true?

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