
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 $a=(\frac{1}{8})^{-1}$, $b=\left(2024-\pi \right)^{0}$, $c=|1-\sqrt{3}|$, $d=\sqrt{3}×3$.  
$(1)$ Simplify these four numbers;  
$(2)$ Based on the simplified results, express the difference between the sum of rational numbers and the product of irrational numbers in these four numbers, then calculate the result.

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