
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  $A=\{a^3+b^3+c^3-3abc|a,b,c\in\mathbb{N}\}$ ,  $B=\{(a+b-c)(b+c-a)(c+a-b)|a,b,c\in\mathbb{N}\}$ ,  $P=\{n|n\in A\cap B,1\le n\le 2016\}$ , find the value of  $|P|$ .

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