
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 integers \( a \) and \( b \) have the property that the expression

\[ \frac{2n^3 + 3n^2 + an + b}{n^2 + 1} \]

is an integer for every integer \( n \). What is the value of the expression above when \( n = 4 \)?

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