
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]


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In an opaque box, there are four small balls that are identical except for their colors. The probability of having two red balls and two white balls is $\frac{2}{3}$, and the probability of having three red balls and one white ball is $\frac{1}{3}$. <br/>$(1)$ If one ball is randomly drawn from the box, find the probability of drawing a red ball; <br/>$(2)$ Now, two or three balls are randomly drawn from the box at once. It is known that the probability of drawing two balls is $\frac{3}{4}$, and the probability of drawing three balls is $\frac{1}{4}$. Each red ball is worth 2 points, and each white ball is worth -1 point. Let $X$ represent the sum of the points of the drawn balls. Find the distribution table of $X$ and its expected value.

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