
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
Karel, Mirek, and Luděk compared their stamp collections. When checking the counts, they found that Karel and Mirek together have 101 stamps, Karel and Luděk have 115 stamps, and Mirek and Luděk have 110 stamps. When verifying what could be changed, they found out that no stamp is shared among all three, but Karel and Mirek have 5 identical stamps, Karel and Luděk have 12 identical stamps, and Mirek and Luděk have 7 identical stamps.

How many stamps does Luděk have that are different from those of the other boys?

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