
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 for the first time. At any point $(a,b)$, the particle randomly moves to $(a-1,b)$, $(a,b-1)$, or $(a-1,b-1)$, with each move having an equal probability of $\frac{1}{3}$. Determine the probability that the particle first hits the coordinate axes exactly at $(0,0)$.

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