
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
Given that the frog starts at point $(2, 1)$ on a square with vertices at $(0,0)$, $(0,5)$, $(5,5)$, and $(5,0)$, and makes jumps of length $1$ with probabilities $\frac{3}{5}$ for vertical and $\frac{2}{5}$ for horizontal jumps, calculate the probability that the frog's sequence of jumps ends on a horizontal side of the square.

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