
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 distinct red balls and 6 distinct white balls (all balls are of the same size).  
(1) How many different ways can you draw 3 balls from the bag such that all balls are of the same color?  
(2) If drawing a red ball scores 2 points and drawing a white ball scores 1 point, how many different ways can you draw 5 balls from the bag so that the total score is at least 7 points?

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