
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
Let $m$ and $n$ be natural numbers not greater than 6. Determine the number of hyperbolas represented by the equation $C_6^m x^2 - C_6^n y^2 = 1$.

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