
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 in a row: the first and third contain orange juice, while the second and fourth are empty. While waiting for guests, Valya absent-mindedly and randomly transfers 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 transfers needed for the first and third glasses to become empty and the second and fourth glasses to become full.

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