
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
Set \( A = \{1, 2, \cdots, n\} \). If there exist nonempty sets \( B \) and \( C \) such that \( B \cap C = \emptyset \), \( B \cup C = A \), and the sum of the squares of the elements in \( B \) is \( M \), and the sum of the squares of the elements in \( C \) is \( N \), and \( M - N = 2016 \), find the smallest value of \( n \).

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