
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
In a certain middle school, the number of boys is $1.5$ times the number of girls. After investigation, it was found that $40\%$ of boys like sports, and $20\%$ of girls like sports. Now, a student is randomly selected from this middle school.  
$(1)$ Find the probability that this student likes sports.  
$(2)$ Given that this student likes sports, find the probability that the student is a boy.

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