
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 12th roll is her last roll, and both the 11th and 12th rolls are a 4? Express your answer as a decimal to the nearest thousandth.

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