
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
By eliminating \(u\) and \(v\) from the equations \(u - v = a\), \(u^2 - v^2 = b\), and \(u^3 - v^3 = c\), find the relationship between \(a\), \(b\), and \(c\).

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