
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 at random to one of the points \( (a-1,b) \), \( (a,b-1) \), or \( (a-1,b-1) \), each with probability \( \frac{1}{3} \). Find the probability that it will hit the coordinate axes at \( (0,0) \).

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