
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 that the function $f(x)$ has the following properties on the set of real numbers $\mathbb{R}$: (1) The line $x = 1$ is an axis of symmetry for the function $f(x)$; (2) $f(x + 2) = -f(x)$; (3) When $1 \leq x\_1 < x\_2 \leq 3$, $[f(x\_2) - f(x\_1)] \cdot (x\_2 - x\_1) < 0$. Determine the order of $f(2015)$, $f(2016)$, and $f(2017)$ from largest to smallest.

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