
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 a frog that begins its journey on pad 2, and when on pad N, jumps to pad N-1 with probability \(\frac{2N}{15}\) and to pad N+1 with probability \(1 - \frac{2N}{15}\), where 0 < N < 14, calculate the probability that the frog escapes without being eaten.

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