
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
Samantha writes the numbers $1,2,3, \dots,49, 50$. She skips the first number $(1)$, marks out the next number $(2)$, skips $3$, marks out $4$, and repeats this skipping and marking to the end of the list. Then she starts again at the beginning of her list, skips the first remaining number $(3)$, marks the next number $(5)$, skips $7$, marks $9$, and continues this pattern to the end. Samantha continues in this manner, each time starting the round by skipping the first unmarked, unskipped number of the last round’s remaining list, then marking the next, until only one number remains. What is that number?

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