
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

The sets $A$ and $B$ are defined as follows:
$$
\begin{aligned}
A= & \left\{a^{3}+b^{3}+c^{3}-3 a b c \mid a, b, c \in \mathbf{N}\right\}, \\
B= & \{(a+b-c)(b+c-a)(c+a-b) \mid \\
& a, b, c \in \mathbf{N}\} .
\end{aligned}
$$

Let the set $P=\{n \mid n \in A \cap B, 1 \leqslant n \leqslant 2016\}$. Find the number of elements in $P$.

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