
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
The teacher wrote four different natural numbers in the notebook. For each pair of these numbers, Peter found their greatest common divisor. He ended up with six numbers: 1, 2, 3, 4, 5, and \( N \), where \( N > 5 \). What is the smallest possible value of \( N \)?

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