
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
An influenza outbreak occurred in regions $A$, $B$, and $C$. The percentages of people with influenza in these three regions are $6\%$, $5\%$, and $4\%$ respectively. It is assumed that the populations of these three regions are in the ratio of $3:5:2$. Now, a person is randomly selected from these three regions.  
$(1)$ Find the probability that this person has influenza.  
$(2)$ If this person has influenza, find the probability that this person is from region $A$.

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