
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 \((m, n)\) be a pair of positive integers. Julia has carefully planted \(m\) rows of \(n\) dandelions in an \(m \times n\) array in her back garden. Now, Jana and Viviane decide to play a game with a lawnmower they just found. Taking alternating turns and starting with Jana, they can mow down all the dandelions in a straight horizontal or vertical line (and they must mow down at least one dandelion!). The winner is the player who mows down the final dandelion. Determine all pairs \((m, n)\) for which Jana has a winning strategy.

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