
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
A math professor asks 100 math students to guess an integer between 0 and 100, inclusive, such that their guess is 'two-thirds of the average of all the responses.' Each student who guesses the highest integer that is not higher than two-thirds of the average of all responses will receive a prize. Assuming that it is common knowledge that all students will write down the best response, and there is no communication between students, what single integer should every student write down?

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