
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 3 cards, which are the red 3, red 4, and black 5 (referred to as red 3, red 4, black 5). After shuffling the cards, player A draws a card first, notes the suit and number, then returns the card, shuffles again, and player B draws a card.  
$(1)$ The probability of drawing two cards both being hearts (please use "tree diagram" or "list" methods to write the analysis process);  
$(2)$ Players A and B play a game with two scenarios. Scenario $A$: player A wins if the suits drawn are the same, otherwise player B wins. Scenario $B$: player A wins if the sum of the numbers drawn is odd, otherwise player B wins. Which scenario has a higher winning rate for player A?

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