
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
Consider a number line, with a lily pad placed at each integer point. A frog is standing at the lily pad at the point 0 on the number line, and wants to reach the lily pad at the point 2014 on the number line. If the frog stands at the point \( n \) on the number line, it can jump directly to either point \( n+2 \) or point \( n+3 \) on the number line. Each of the lily pads at the points \( 1, \ldots, 2013 \) on the number line has, independently and with probability \( \frac{1}{2} \), a snake. Let \( p \) be the probability that the frog can make some sequence of jumps to reach the lily pad at the point 2014 on the number line, without ever landing on a lily pad containing a snake. What is \( p^{1 / 2014} \)? Express your answer as a decimal number.

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