
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 the values of \(a\) and \(b\) such that the equation \((x + m)^3 - (x + n)^3 = (m - n)^3\) holds, where \(m\) and \(n\) are unequal non-zero constants, and \(x = am + bn\).

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