
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
Stefan Banach and matches. According to an improbable legend, one day in a small shop in the center of Lviv, Stefan Banach bought two matchboxes and put them in his jacket pocket. Each box contained 60 matches.

When Banach needs a match, he randomly picks a box and takes a match from it. At some moment, Banach picked a box and found it empty. Find the mathematical expectation of the number of matches in the other box.

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