
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  $m\times{n}$  grid are there are token. Every  token *dominates* every square on its same row ( $\leftrightarrow$ ), its same column ( $\updownarrow$ ), and diagonal ( $\searrow\hspace{-4.45mm}\nwarrow$ )(Note that the token does not \emph{dominate} the diagonal ( $\nearrow\hspace{-4.45mm}\swarrow$ ), determine the lowest number of tokens that must be on the board to *dominate* all the squares on the board.

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