
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
In a basketball all-star game, there are 27 players participating, each wearing a jersey with their favorite number printed on it. Each number is a non-negative integer. After the game, they form a team lineup in 3 rows and 9 columns for fans to take photos. A quirky fan only takes photos where the players in the shot form a rectangular block of \(a\) rows and \(b\) columns (\(1 \leqslant a \leqslant 3\), \(1 \leqslant b \leqslant 9\)) such that the sum of the jersey numbers of the players within the frame is a multiple of 10. As a result, the fan captures only \(s\) players in total. Find the minimum possible value of \(s\).

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