
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 $m$ and $n$ be two odd integers with $m, n \geqslant 3$. In an $m \times n$ grid, each small square is colored either blue or red. We denote $A$ as the number of rows where blue squares are in the majority, and $B$ as the number of columns where red squares are in the majority.

What is the largest possible value of $A + B$?

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