
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
In a school corridor, there is a row of lockers numbered from 1 to 500. Initially, all lockers are closed. A student starts at locker 1, opens it, and then proceeds by skipping one locker and opening the next, continuing this pattern until he reaches the end of the corridor. Upon reaching the end, he turns around, skips the first closed locker he sees, then opens the next closed locker, and continues alternating skipping and opening each subsequent closed locker. The student repeats this process of turning around whenever he reaches an end and continuing the pattern until only one locker remains closed. Which is the last locker he opens?

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