
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 starts at the point $(5,5)$ and moves until it hits one of the coordinate axes. When the particle is at the point $(a,b)$, it moves randomly to one of the points $(a-1,b)$, $(a,b-1)$, or $(a-1,b-1)$, each with probability $\frac{1}{3}$. Calculate the probability that it will hit the coordinate axes at $(0,0)$.

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