
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 is at the point (2, 3) in a square region bounded by (1,1), (1,6), (6,6), and (6,1). Each jump is either up, down, left, or right by 1 unit. If the frog reaches (3,3) or (4,3), its next two jumps must be in the same direction (vertical or horizontal, corresponding to the last jump). Determine the probability that the frog's sequence of jumps ends on the top or bottom boundary of the square.

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