
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 contain orange juice, and the second and fourth are empty. In anticipation of guests, Valya absent-mindedly 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, after which the configuration becomes the reverse: the first and third are empty, and the second and fourth are full.

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