
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
Arthur Gombóc lives at 1 Édes Street, and the chocolate shop is at the other end of the street, at number $n$. Each day, Arthur performs the following fitness routine: he starts from house number 2. If he is standing in front of house number $k$ (where $1 < k < n$), he flips an expired but fair chocolate coin. If it lands heads, he moves to house number $(k-1)$, and if it lands tails, he moves to house number $(k+1)$. If he reaches the chocolate shop, he goes in and eats a chocolate ball, then moves to house number $(n-1)$. If he reaches home, the exercise is over. On average, how many chocolate balls does Arthur eat each day?

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