
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
From the set $\{1,2,3,...,11\}$, two elements are chosen as $m$ and $n$ for the elliptic equation $\frac{x^2}{m^2} + \frac{y^2}{n^2} = 1$. Calculate the number of unique ellipses that can be formed within the rectangular region $B = \{(x,y) \mid |x| < 11, |y| < 9\}$.

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