
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 the dot labeled $A$ on a square grid with 5 horizontal lines and 5 vertical lines. Each minute, the ant randomly moves to any of the connected neighboring dots. Determine the probability that, after 10 minutes, the ant ends up at the dot labeled $B$. Assume that all dots on horizontal and vertical midlines are blue; others are red. $A$ is at the center and $B$ is on a neighboring blue dot directly to the north of $A$.
\[ \text{[diagram omitted for clarity]} \]

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