
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
A sequence  $a_n$  is defined by  $$ a_0=0,\qquad a_1=3; $$    $$ a_n=8a_{n-1}+9a_{n-2}+16\text{ for }n\ge2. $$  Find the least positive integer  $h$  such that  $a_{n+h}-a_n$  is divisible by  $1999$  for all  $n\ge0$ .


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