
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 lottery, predictions need to be made for 12 matches in each case with the symbols $\gg 1 \ll$, $\gg 2 \ll$, or $\gg \mathrm{x} \ll$. What is the expected number of correct guesses if we fill out the ticket randomly (e.g., based on a draw) in such a way that each of the three outcomes has an equal chance for each match?

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