
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
The sequence $\{a_n\}$ satisfies $a_{n+2} = 2a_{n+1} - a_n$, and $a_{2014}, a_{2016}$ are the extremum points of the function $f(x) = \frac{1}{3}x^3 - 4x^2 + 6x - 1$. Calculate the value of $\log_2(a_{2000} + a_{2012} + a_{2018} + a_{2030})$.

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