
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
In the Cartesian coordinate plane, points whose x-coordinates and y-coordinates are both integers are called lattice points. There is a series of isosceles right triangles △OA<sub>1</sub>B<sub>1</sub>, △OA<sub>2</sub>B<sub>2</sub>, △OA<sub>3</sub>B<sub>3</sub>, ..., △OA<sub>n</sub>B<sub>n</sub>, ..., where point O is the origin, the right-angle vertex A<sub>n</sub> has coordinates (n, n) (n∈N<sup>*</sup>, n≥3), and point B<sub>n</sub> is on the positive x-axis. The number of lattice points inside the nth isosceles right triangle △OA<sub>n</sub>B<sub>n</sub> (excluding the boundary) is.

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