
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
Mr. Alex plays the following game: at the start, there are nine empty boxes in a row. Each turn, Alex can choose one of the following two options:
(1) Choose any number of the form \(2^j\) (where \( j \in \mathbf{N} \)) and place this number in an empty box;
(2) Choose two boxes containing the same number (they do not need to be adjacent), denote this number as \(2^j\) (where \( j \in \mathbf{N} \)), then replace the number in one box with \(2^{j+1}\) and remove the number from the other box.

At the end of the game, one box contains the number \(2^n\) (where \(n\) is a given positive integer) and the remaining boxes are empty. Determine the maximum number of operations Alex can perform (expressed in terms of \(n\)).

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