
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 $C$ are vertices of an isosceles triangle with $AB = AC$. Points $M$, $N$, and $P$ are placed such that $M$ is the midpoint of $AB$, $N$ divides side $AC$ into segments in the ratio $1:2$ starting from $A$, and $P$ divides side $BC$ into segments in the ratio $1:3$ starting from $B$. How many non-congruent triangles can be drawn using any three of these six points as vertices?

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