
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
Find all pairs of natural numbers \(a\) and \(b\) such that \(\frac{a^{2}+b}{b^{2}-a}\) and \(\frac{b^{2}+a}{a^{2}-b}\) are integers.

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