
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
Alice places down  $n$  bishops on a  $2015\times 2015$  chessboard such that no two bishops are attacking each other.  (Bishops attack each other if they are on a diagonal.)

[list=a]
[*]Find, with proof, the maximum possible value of  $n$ .
[*](A1 only) For this maximal  $n$ , find, with proof, the number of ways she could place her bishops on the chessboard.
[/list]

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