
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 7 paper slips labeled with numbers 1, 2, 3, 4, 5, 6, 7. Xiao Ming draws one slip randomly (without replacement) from the set, and then Xiao Ying draws one slip from the remaining slips. The person who draws the slip with the larger number wins. The slips are then returned, and the game restarts.  
$(1)$ If Xiao Ming has already drawn the slip labeled 4, and then Xiao Ying draws a slip, what is the probability that Xiao Ming wins? What is the probability that Xiao Ying wins?  
$(2)$ If Xiao Ming has already drawn the slip labeled 6, what are the probabilities of Xiao Ming and Xiao Ying winning, respectively?

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