
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
Fibonacci, a renowned Italian mathematician, explored the problem of rabbit population growth and discovered a sequence of numbers: 1, 1, 2, 3, 5, 8, 13,…, where starting from the third number, each number is the sum of the two preceding numbers. This sequence, denoted as $\{a_n\}$, is called the "Fibonacci sequence." It is a very beautiful and harmonious sequence with many wonderful properties. For instance, as the number of terms increases, the ratio of a term to its successor approaches the golden ratio 0.6180339887. If we take each term in the sequence $\{a_n\}$ and find the remainder when divided by 4, to form a new sequence $\{b_n\}$, what is the value of the 2016th term in sequence $\{b_n\}$?

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