
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
$71 N$ is a positive integer. In the square $R$ with vertices at $(N, 0)$, $(0, N)$, $(-N, 0)$, and $(0, -N)$ (including the boundary), there are _____ lattice points.

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