
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 down a hallway with a row of closed lockers, numbered from 1 to 500. Initially, she opens every second locker. On returning, she toggles every third locker (i.e., she opens it if it's closed and closes it if it's open). If a locker ends up being closed at the end of this pass, she continues the process by toggling every fourth locker. She repeats this process by increasing the step by one each time (i.e., fifth, sixth, etc.) until all lockers are open. What is the number of the last locker she opens?

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