
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 exam, three sets of questions, denoted as $A$, $B$, and $C$, were prepared. Before the exam, one set of questions was randomly selected as the exam paper. The probabilities of selecting question sets $A$ and $B$ were both $0.3$. If the exam paper is either $A$ or $C$, the probability of student $A$ passing is $0.8$. If the exam paper is $B$, the probability of student $A$ passing is $0.6$. What is the probability that student $A$ will pass the exam?

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