
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 student walks down a hall with a row of 2048 closed lockers, numbered from $1$ to $2048$. Initially, he opens every second locker (i.e., lockers 2, 4, 6, ...). Upon reaching the end, he turns around, skips one locker, and then opens the first closed locker and every third locker after that (i.e., he opens every third closed locker on his way back). The student continues this pattern of increasing the number of skipped lockers by one each time he reaches the end of the hall until all lockers are opened. Determine the number of the last locker he opens.

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