
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
Let  $ABCD$  be a regular tetrahedron. Suppose points  $X$ ,  $Y$ , and  $Z$  lie on rays  $AB$ ,  $AC$ , and  $AD$  respectively such that  $XY=YZ=7$  and  $XZ=5$ . Moreover, the lengths  $AX$ ,  $AY$ , and  $AZ$  are all distinct. Find the volume of tetrahedron  $AXYZ$ .

*Proposed by Connor Gordon*

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