
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, four glasses are arranged in a row: the first and third contain orange juice, while the second and fourth are empty. While waiting for guests, Valya absentmindedly and randomly pours juice from one glass to another. Each time, she can take a full glass and pour all its contents into one of the two empty glasses.

Find the expected number of pourings required for the situation to be completely reversed: the first and third glasses empty, while the second and fourth glasses are full.

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