
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
In a pond, there are thirteen lily pads in a row labeled from 0 to 12. A frog starts on pad 3. When the frog is on pad \(N\) where \(0 < N < 12\), it jumps to pad \(N-1\) with a probability of \(\frac{N+1}{13}\) and to pad \(N+1\) with \(\frac{12-N}{13}\). If the frog reaches pad 0, it gets caught by a snake. If it reaches pad 12, it escapes safely. What is the probability that the frog will escape without being caught by the snake?
A) $\frac{13}{19}$
B) $\frac{112}{164}$
C) $\frac{55}{121}$
D) $\frac{60}{105}$

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