
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
Given \(\log _{a} x + 3 \log _{x} a - \log _{x} y = 3 \ (a > 1)\),
(1) Let \(x = a^{t}\), express \(y\) in terms of \(a\) and \(t\);
(2) If \(y\) has a minimum value of 8 when \(0 < t \leqslant 2\), find \(a\) and \(x\).

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