
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 a right triangle with side lengths $AB = 3$, $BC = 4$, and $AC = 5$, making $C$ the right angle. Points $P$, $Q$, and $R$ are the midpoints of sides $AB$, $BC$, and $AC$ 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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