
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
12 teachers each made a guess about the answer to this question. Their guesses were: "not less than 1", "not more than 2", "not less than 3", "not more than 4", "not less than 11", "not more than 12" (with "not less than" followed by an odd number and "not more than" followed by an even number). How many teachers guessed the correct answer?

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