
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 every second locker (i.e., locker 2, 4, 6...2048). When he reaches the end of the hall, he turns around and starts back, now opening every third closed locker he encounters. The student continues this pattern, increasing the skip number by one each time he reaches the start of the hall and turns around, until every locker is open. What is the number of the last locker he opens?

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