
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
Consider a simplified grid of size $2 \times 2$. Frieda the frog starts in the top-left corner and hops randomly choosing one of three possible movements with equal probability: moving right, moving down, or staying in the same cell (no diagonal moves). She must make exactly three hops. Calculate the probability that she ends up in the same corner where she started.

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