
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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A class has $6$ officials, of which $4$ are male and $2$ are female. Three people are selected to participate in the school's mandatory labor.

$(1)$ Calculate the probability that male student A or female student B is selected.

$(2)$ Let event $A$ be "male student A is selected," and let event $B$ be "female student B is selected." Calculate $P(A)$ and $P(B \mid A)$.

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