
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
There are several identical balls except for their colors. $10$ balls are selected from them to play a game of drawing balls and putting them into an opaque bag.<br/>$(1)$ If the bag contains $5$ red balls, $2$ white balls, and $3$ yellow balls, the probability of drawing a red ball is ______;<br/>$(2)$ Xiaoming and Xiaoliang play a game together. If the bag contains $4$ red balls and $6$ white balls, Xiaoming wins by drawing a red ball, and Xiaoliang wins by drawing a white ball. Is this game fair? Explain your reasoning;<br/>$(3)$ Xiaoying randomly draws a ball from the bag described in $(2)$ and finds it to be a white ball. If this white ball is not put back, and then another ball is randomly drawn from the bag, the probability of drawing a white ball is ______.

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