
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
On the New Year's table, there are 4 glasses arranged in a row: the first and third glasses contain orange juice, while the second and fourth glasses are empty. In anticipation of guests, Valya absentmindedly and randomly pours juice from one glass to another. Each time, she can take a full glass and pour its entire contents into one of the two empty glasses.

Find the expected number of pourings needed to achieve the opposite situation: the first and third glasses are empty, while the second and fourth glasses are full.

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