
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
A pocket contains $4$ distinct red balls and $7$ distinct white balls.

$(1)$ How many ways are there to select $4$ balls such that the number of red balls is not less than the number of white balls?

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

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