
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
Let \( A \) be a 3x9 grid where each cell is filled with a positive integer. A \( m \times n \) (where \( 1 \leq m \leq 3 \) and \( 1 \leq n \leq 9 \)) sub-grid within \( A \) is called a "good rectangle" if the sum of the numbers within it is a multiple of 10. A \( 1 \times 1 \) cell is called a "bad cell" if it is not contained in any "good rectangle". Find the maximum number of "bad cells" in \( A \).

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