
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 bag contains $4$ red balls and $6$ white balls of the same size. Four balls are drawn from the bag. (Write out the solution steps and express the final result in numerical form.)
$(1)$ How many different ways are there to draw the balls if they must be of two colors?
$(2)$ How many different ways are there to draw the balls if the number of red balls drawn is not less than the number of white balls drawn?

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