
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 \\(f(x)\\) is an even function defined on \\(\mathbb{R}\\), and for \\(x \geqslant 0\\), \\(f(x+1) = -f(x)\\), and when \\(x \in [0,1)\\), \\(f(x) = \log_{2}(x+1)\\), the correct statement(s) is/are \_\_\_\_\_\_\_\_\_. 

\\(①\\) \\(f(2016) + f(-2017) = 0\\);          

\\(②\\) The function \\(f(x)\\) is periodic with a period of \\(2\\) over its domain;

\\(③\\) The line \\(y=x\\) intersects the graph of the function \\(f(x)\\) at \\(2\\) points;        

\\(④\\) The range of the function \\(f(x)\\) is \\((-1,1)\\).

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