
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
Let  $(a_n)_{n \geq 0}$  be the sequence of integers defined recursively by  $a_0 = 0, a_1 = 1, a_{n+2} = 4a_{n+1} + a_n$  for  $n \geq 0.$  Find the common divisors of  $a_{1986}$  and  $a_{6891}.$ 

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