
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 jumping from the point \((1,2)\) and makes a series of jumps, each of which is parallel to one of the coordinate axes and is 1 unit in length. Knowing that the direction of each jump (up, down, right, or left) is chosen at random, the frog stops jumping when it reaches the boundary of the square with vertices \((0,0)\), \((0,4)\), \((4,4)\), and \((4,0)\), calculate the probability that the frog ends its jumps on a vertical side of the square.

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