
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
There are 240 students participating in a large group performance. They stand in a line facing the coach and count off from left to right as $1, 2, 3, 4, 5, \cdots$, and so on. The coach requires all students to remember their reported number and perform the following actions: first, all students whose numbers are multiples of 3 turn around; next, all students whose numbers are multiples of 5 turn around; finally, all students whose numbers are multiples of 7 turn around. 

Questions:
(1) How many students are still facing the coach?
(2) Among the students facing the coach, what is the number reported by the 66th student from the left?

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