
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 the sequence \(\left\{x_{n}\right\}\) be defined by \(x_{1}=1\) and \(x_{n+1}=4 x_{n}+\left\lfloor \sqrt{11} \, x_{n} \right\rfloor\). Find the units digit of \(x_{2012}\).

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