
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
There are \( n \) people standing in a row, numbered from left to right as \( 1, 2, \cdots, n \). Those whose numbers are perfect squares will leave the line. The remaining people will then renumber themselves from left to right again as \( 1, 2, \cdots \), and those whose new numbers are perfect squares will leave the line again. This process continues until everyone has left the line. Define \( f(n) \) as the original number of the last person to leave the line. Find an expression for \( f(n) \) in terms of \( n \), and find the value of \( f(2019) \).

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