
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 a bag, there are $5$ different red balls and $4$ different white balls.<br/>$(1)$ If all the balls are taken out of the bag and lined up in a row, find the number of ways to arrange the white balls so that they are not adjacent to each other;<br/>$(2)$ It is known that taking out a red ball scores $2$ points, and taking out a white ball scores $1$ point. If $5$ balls are taken out from the bag, and the total score is at least $8$ points, find the number of different ways to do so.

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