
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
Sabrina has a fair tetrahedral die whose faces are numbered 1, 2, 3, and 4, respectively.  She creates a sequence by rolling the die and recording the number on its bottom face.  However, she discards (without recording) any roll such that appending its number to the sequence would result in two consecutive terms that sum to 5.  Sabrina stops the moment that all four numbers appear in the sequence.  Find the expected (average) number of terms in Sabrina's sequence.

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