
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
An infinite sequence of positive real numbers is defined by  $a_0=1$  and  $a_{n+2}=6a_n-a_{n+1}$  for  $n=0,1,2,\cdots$ .  Find the possible value(s) of  $a_{2007}$ .

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