
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 $4$ different red balls and $6$ different white balls.  
$(1)$ If $4$ balls are randomly selected from the bag, how many ways are there to select the balls such that the number of red balls is not less than the number of white balls?  
$(2)$ If a red ball is worth $2$ points and a white ball is worth $1$ point, how many ways are there to select $5$ balls from the bag such that the total score is at least $7$ points?

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