
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
The sequence  $\{a_{n}\}_{n\geq 0}$  is defined by  $a_{0}=20,a_{1}=100,a_{n+2}=4a_{n+1}+5a_{n}+20(n=0,1,2,...)$ . Find the smallest positive integer  $h$  satisfying  $1998|a_{n+h}-a_{n}\forall n=0,1,2,...$ 

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