
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 lined with 2048 closed lockers numbered 1 to 2048. He starts at locker 1, opens it, and then alternates between skipping one and opening the next throughout the entire row. When reaching the end, he turns around, opens the first closed locker he sees, and continues the pattern of skipping one and opening the next among the closed lockers. He repeats this process back and forth until all lockers are open. Determine the number of the last locker he opens.

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