
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

Vasya and Misha took a test consisting of 20 questions of equal difficulty, each with multiple-choice answers. Since neither Vasya nor Misha knew the answers, they only guessed. Vasya guessed correctly on 6 questions, while Misha guessed correctly on 8 questions, independently from Vasya. Find the expected number of coincidences, that is, the number of questions where both Vasya and Misha either guessed correctly or incorrectly.

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