
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
 $n$  symbols line up in a row, numbered as  $1,2,...,n$  from left to right. Delete every symbol with squared numbers. Renumber the rest from left to right. Repeat the process until all  $n$  symbols are deleted. Let  $f(n)$  be the initial number of the last symbol deleted. Find  $f(n)$  in terms of  $n$  and find  $f(2019)$ .

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