
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 3000 pieces placed on the circumference of a circle, numbered sequentially in a clockwise direction as $1, 2, 3, \cdots, 2999, 3000$. First, piece number 3 is removed. Then, moving clockwise, every 2nd piece is removed, continuing this process until piece number 1 is removed. At that point:

(1) How many pieces are left on the circumference?
(2) Among the remaining pieces, what is the number of the 181st piece, starting from the smallest numbered piece?

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