
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 $28 \times 35$ table, some $k$ cells are colored red, some $r$ cells are colored pink, and the remaining $s$ cells are colored blue. It is known that:

- $k \geqslant r \geqslant s$
- Each boundary cell has at least 2 neighbors of the same color
- Each non-boundary cell has at least 3 neighbors of the same color

What is the smallest possible value of $k - s$?

(A cell is called a boundary cell if it is adjacent to the border of the table. Neighbors are cells that share a common side.)

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