
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 along a corridor of lockers numbered from $1$ to $2048$. Initially, all lockers are closed. He starts by opening every locker. On his return trip, he skips one locker and opens the next. When he reaches the beginning again, he skips two lockers and opens the next closed locker, and continues this pattern. He repeats this pattern, increasing the skip by one each time until all lockers are open. What is the number of the last locker he opens?

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