
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
Consider  $f_1=1, f_2=1$  and  $f_{n+1}=f_n+f_{n-1}$  for  $n\geq 2$ . Determine if exists  $n\leq 1000001$  such that the last three digits of  $f_n$  are zero.

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