
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
Given an even function $f(x)\colon \mathbb{Z} \to \mathbb{Z}$ satisfying $f(1)=1$, $f(2015) \neq 1$, and for any integers $a$, $b$, we have $f(a+b) \leq \max\{f(a),f(b)\}$, find the value of $f(2016)$.

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