
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 $6$ red balls and $4$ white balls of the same size. Now, $4$ balls are randomly drawn from the bag. <br/>$(1)$ Find the probability that the number of red balls drawn is greater than the number of white balls drawn; <br/>$(2)$ If a red ball is worth $2$ points and a white ball is worth $1$ point, let $X$ represent the total score of the $4$ balls drawn. Find the probability distribution and the expected value of the random variable $X$.

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