
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
Points $A$, $B$, and $C$ represent an isosceles triangle with $AB=AC$ and base $BC$. Points $M$, $N$, and $O$ are midpoints of sides $AB$, $AC$, and $BC$, respectively. Determine the number of noncongruent triangles that can be formed using any three of these six points as vertices.

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