
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
It is known that all faces of a tetrahedron are similar, but not all of them are equal triangles. In addition, any two faces share at least one pair of equal edges, not including the common edge. Find the volume of this tetrahedron if the lengths of two edges lying in one face are 3 and 5.

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