
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  $(0,0,0)$  in three-dimensional space. Each second, it randomly selects one of the eight lattice points a distance of  $\sqrt{3}$  from its current location and moves to that point. What is the probability that, after two seconds, the particle is a distance of  $2\sqrt{2}$  from its original location? 

*Proposed by Connor Gordon*

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