
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
Three numbers are arranged in order: $3$, $9$, $8$. For any two adjacent numbers, subtract the left number from the right number to get the difference, and write it between these two numbers. This process generates a new sequence: $3$, $6$, $9$, $-1$, $8$, which is called the first operation. The same operation can be applied again to generate a new sequence after the second operation: $3$, $3$, $6$, $3$, $9$, $-10$, $-1$, $9$, $8$. Continue this operation. Find:<br/>$(1)$ After the first operation, what is the sum of all the new numbers added?<br/>$(2)$ How much is the sum of all the new numbers added in the second operation compared to the first operation?<br/>$(3)$ Conjecture: What is the sum of all the new numbers added in the sequence obtained after the one hundredth operation compared to the sequence obtained after the ninety-ninth operation?

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