
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 number of triangles with vertices' coordinates $(x, y)$ that satisfy $1 \leqslant x \leqslant 4, 1 \leqslant y \leqslant 4$, and where $x$ and $y$ are integers is $\qquad$ .

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