
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
There are two triangles with side lengths $3, 4, 5$, four triangles with side lengths $4, 5, \sqrt{41}$, and six triangles with side lengths $\frac{5}{6} \sqrt{2}, 4, 5$. Using these triangles as faces, how many tetrahedrons can be formed?

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