
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
An ant starts at point $A$ on a cubic lattice grid. It moves randomly every minute to any adjacent point (including up or down if on a middle floor). Calculate the probability that after four minutes the ant is at point $B$, directly one floor above its starting point $A$. Assume the cubic grid extends indefinitely in all directions.

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