
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
Consider the region in the plane represented by the system of inequalities $\begin{cases} y \leqslant x, \ 0 < x \leqslant 3, \ y > \frac{1}{x} \end{cases}$. If three points with integer coordinates (lattice points) are randomly chosen from this region, the probability that these three points form a triangle is \_\_\_\_\_\_\_.

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