
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
A frog starts at the point (2, 3) on a coordinate plane and makes jumps of length 2. Each jump can be either up, down, left, or right with the probabilities of jumping left or right being $\frac{1}{3}$ each, and the probabilities of jumping up or down being $\frac{1}{6}$ each. Determine the probability that the sequence of jumps ends on one of the vertical sides of the rectangle defined by (0, 0), (0, 6), (6, 6), and (6, 0).

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