
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
A bored student walks down a hall that contains a row of closed lockers, numbered $1$ to $2048$. He opens the locker numbered 1, then skips two lockers and opens the next one, and continues this pattern. When he reaches the end of the hall, the student turns around and starts back. He opens the first closed locker he encounters, skips two closed lockers, opens the next closed locker, and continues this pattern. The student keeps wandering back and forth in this manner until every locker is open. What is the number of the last locker he opens?

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