
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
In the tetrahedron \(ABCD\), it is known that \(AD \perp BC\),
\[ 
\begin{aligned}
AD &= 6, \\
BC &= 2, \text{ and} \\
AB + BD &= AC + CD = t \quad (t \in [8, +\infty)).
\end{aligned}
\]
Determine the range of the maximum volume of tetrahedron \(BCDA\).

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