
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 \(a_{n+2}=6 a_{n}-a_{n+1}\) for \(n=0,1,2, \cdots\). Find the possible value(s) of \(a_{2007}\).

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