
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
One hundred students, each wearing a shirt with a number, stood in a circle in the following sequence: \(1, 2, 3, \ldots, 100\). Upon a command, they started leaving in this manner: the student with the number 1 stays, the student with number 2 leaves, the student with number 3 stays, the student with number 4 leaves, and so on, every other student in the circle, until only one student remains. What number is on the shirt of the last remaining student?

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