
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
Define a sequence of functions recursively by  $f_1(x) = |x-1|$  and  $f_n(x)=f_{n-1}(|x-n|)$  for integers  $n > 1$ . Find the least value of  $n$  such that the sum of the zeros of  $f_n$  exceeds  $500{,}000$ .


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