
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
Twelve numbers \(a_{i}\) form an arithmetic progression, such that \(a_{k} + d = a_{k+1}\). Find the volume of the tetrahedron with vertices at the points \(\left(a_{1}^{2}, a_{2}^{2}, a_{3}^{2}\right),\left(a_{4}^{2}, a_{5}^{2}, a_{6}^{2}\right), \left(a_{7}^{2}, a_{8}^{2}, a_{9}^{2}\right),\left(a_{10}^{2}, a_{11}^{2}, a_{12}^{2}\right)\).

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