
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  $x_1=y_1=x_2=y_2=1$ , then for  $n\geq 3$  let  $x_n=x_{n-1}y_{n-2}+x_{n-2}y_{n-1}$  and  $y_n=y_{n-1}y_{n-2}-x_{n-1}x_{n-2}$ .  What are the last two digits of  $|x_{2012}|?$ 

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