
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 bag containing $4$ different red balls and $6$ different white balls. Five balls are randomly drawn from the bag. Each red ball drawn is worth $2$ points, and each white ball drawn is worth $1$ point. <br/>$(1)$ How many ways are there to draw the balls such that the total score is at least $7$ points? <br/>$(2)$ If we want to draw $5$ balls with a total score of $8$ points, and arrange them in a row such that only $2$ red balls are adjacent, how many different arrangements are possible?

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