
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
For any two unequal numbers $a$ and $b\left(a \gt b\right)$, a new operation "$\oplus $" is defined as follows: $a\oplus b=\frac{{\sqrt{a+b}}}{{\sqrt{a-b}}}$, for example: $3\oplus 2=\frac{{\sqrt{3+2}}}{{\sqrt{3-2}}}=\sqrt{5}$. Then $12\oplus 4=$____.

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