
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
2011 cards are arranged in a row on a table. One of the numbers '1', '2', and '3' is printed on each card. It is found that there is at least one card between any two cards labelled '1', at least two cards between any two cards labelled '2', and at least three cards between any two cards labelled '3'. If the smallest and greatest possible numbers of cards labelled '3' are \( m \) and \( M \) respectively, find the value of \( m+M \).

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