
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
If Ella rolls a standard six-sided die until she rolls the same number on consecutive rolls, what is the probability that her 15th roll is her last roll? Suppose that for the 15th roll, rolling a 6 has a probability of 1/2 if the 14th roll was a 6, otherwise it follows the standard probability rules.

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