
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
Determine all pairs \((a, b) \in \mathbb{N}\) with \(b \neq 1\) such that

\[ a+1 \mid a^{3} b-1 \quad \text{and} \quad b-1 \mid b^{3} a+1. \]

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