
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
Eighty students stand in a line facing the teacher, and count off from left to right: $1, 2, 3, \cdots, 80$. After the count, the teacher instructs the students whose numbers are multiples of 2 to turn around. Next, the teacher instructs the students whose numbers are multiples of 4 to turn around. Then the multiples of 8 turn around, followed by multiples of 16, 32, and finally 64. How many students are now facing away from the teacher?

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