
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
Given \( P(n) = n^2 + n + 1 \), for any positive integers \( a \) and \( b \), if the set
\[ \{P(a), P(a+1), P(a+2), \cdots, P(a+b)\} \]
has each element not coprime with the product of other elements, then the set is called "fragrant". Find the minimum number of elements in a fragrant set.

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