
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
What is the probability that Frieda ends on any edge square after her three hops on a $4 \times 4$ grid of squares, given that she hops one square in each of the four cardinal directions with equal probability and wraps around if she hops off one edge of the grid?

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