
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 the number of pairs of positive integers  $a$  and  $b$  such that   $a\leq 100\,000$ ,  $b\leq 100\,000$ , and  $$ \frac{a^3-b}{a^3+b}=\frac{b^2-a^2}{b^2+a^2}. $$  

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