
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
\(a, b, m, n\) satisfy: \(a m^{2001} + b n^{2001} = 3\); \(a m^{2002} + b n^{2002} = 7\); \(a m^{2003} + b n^{2003} = 24\); \(a m^{2004} + b m^{2004} = 102\). Find the value of \(m^{2}(n-1)\).

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