
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
A particle begins its journey at point $(5,3)$ and randomly moves to either $(x-1, y)$, $(x, y-1)$, or $(x-1, y-1)$ at each step with a probability of $\frac{1}{3}$ for each direction. The movement stops as soon as the particle hits any of the points $(0,0)$, $(5,0)$, or $(0,3)$. Calculate the probability that the particle stops at $(0,0)$.

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