
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 certain school has $7$ members in its student art department (4 males and 3 females). Two members are to be selected to participate in the school's art performance event.  
$(1)$ Find the probability that only one female member is selected.  
$(2)$ Given that a male member, let's call him A, is selected, find the probability that a female member, let's call her B, is also selected.

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