
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
Consider a table with \( m \) rows and \( n \) columns. In how many ways can this table be filled with all zeros and ones so that there is an even number of ones in every row and every column?

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