
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
An assignment of either a  $ 0$  or a  $ 1$  to each unit square of an  $ m$ x $ n$  chessboard is called  $ fair$  if the total numbers of  $ 0$ s and  $ 1$ s are equal. A real number  $ a$  is called  $ beautiful$  if there are positive integers  $ m,n$  and a fair assignment for the  $ m$ x $ n$  chessboard such that for each of the  $ m$  rows and  $ n$  columns , the percentage of  $ 1$ s on that row or column is not less than  $ a$  or greater than  $ 100\minus{}a$ . Find the largest beautiful number.

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