
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
Ivan Semyonov is taking the Unified State Exam in mathematics. The exam consists of three types of tasks: $A$, $B$, and $C$. Each type $A$ task offers four answer choices, only one of which is correct. There are a total of 10 such tasks. Type $B$ and $C$ tasks require detailed answers. Since Vanya frequently skipped classes, his knowledge of mathematics is shallow. He answers type $A$ tasks by choosing randomly. He solves the first type $B$ task with a probability of $1 / 2$. Vanya cannot do anything more. For each correct answer on a type $A$ task, he receives 1 point, and for a type $B$ task, he receives 2 points. What is the probability that Vanya will score more than 5 points?

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