
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 bored of studying decides to walk down a hallway of 500 lockers, all initially closed and numbered from 1 to 500. Starting from locker 1, the student opens every third locker. Reaching the end, the student turns around and on encountering the first closed locker, begins to open every third closed locker thereafter. The student repeats this pattern of walking back and forth, opening every third closed locker, 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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