
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 a Cartesian coordinate system, the vertices of a square are $(2,2), (-2,2), (-2,-2),$ and $(2,-2)$. A particle starts at $(0,0)$ and moves to one of its eight neighboring integer-coordinate points with equal probability, stopping when it reaches the boundary of the square. Find the probability that the particle ultimately lands on one of the square's vertices.

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