
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 $ABC$ where $AB = AC$ and $BC$ is the base. Points $D$, $E$, and $F$ are the midpoints of $AB$, the midpoint of $AC$, and the foot of the perpendicular from $A$ to $BC$, respectively. How many noncongruent 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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