
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 hall containing a row of closed lockers, numbered $1$ to $729$. He opens every third locker from the start. Once reaching the end, he turns around and opens every third closed locker. This process continues, where each time he only interacts with the third closed locker, until every locker is open. What is the number of the last locker he opens?

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