
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 \(m, n \in \mathbf{N}\) where \(m, n \geq 2\), if \(\frac{2^3-1}{2^3+1} \cdot \frac{3^3-1}{3^3+1} \cdots \frac{n^3-1}{n^3+1} = \frac{m^3-1}{m^3+2}\), find the value of \(m^2 + n^2\).

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