
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
Fang Fang and his classmates play a game where he cuts a piece of paper into 9 pieces, then takes one of those pieces and cuts it into 9 pieces again; then, from those pieces, he takes another piece and cuts it into 9 pieces again; and so on. Can he have exactly 2009 pieces after cutting for the $n$th time? If so, find the value of $n$; if not, explain why.

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