
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 Anchuria, a standardized state exam is conducted. The probability of guessing the correct answer to each exam question is 0.25. In 2011, in order to obtain a certificate, it was necessary to answer correctly three out of 20 questions. In 2012, the School Management of Anchuria decided that three questions were too few. Now it is required to correctly answer six out of 40 questions. The question is, if one knows nothing and simply guesses the answers, in which year is the probability of obtaining an Anchurian certificate higher - in 2011 or in 2012?

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