
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
Black and white coins are placed on some of the squares of a  $418\times 418$  grid.  All black coins that are in the same row as any white coin(s) are removed.  After that, all white coins that are in the same column as any black coin(s) are removed.  If  $b$  is the number of black coins remaining and  $w$  is the number of remaining white coins, find the remainder when the maximum possible value of  $bw$  gets divided by  $2007$ .

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