
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 an exam, the same test consisting of 40 questions was given to each of the three students. A question is called insurmountable if all students answered incorrectly; difficult if only one student answered correctly; easy if exactly two students answered correctly; and trivial if all three students answered correctly. Given that there are twice as many easy questions as insurmountable ones, what is the maximum number of insurmountable questions the test can contain if the total number of correct answers is 64? Justify your answer.

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