
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 $4$ distinct red balls and $6$ distinct white balls.

(I) How many ways are there to draw $4$ balls from the bag such that the number of red balls is not less than the number of white balls?

(II) If drawing a red ball scores $2$ points and drawing a white ball scores $1$ point, how many ways are there to draw $5$ balls from the bag such that the total score is at least $7$ points?

(III) Under the condition of (II), when the total score is $8$ points, how many ways are there to arrange the drawn balls in a row such that only two red balls are adjacent?

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