
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 $x \geq 0$, it satisfies $f(x+1) = -f(x)$. Also, for $x \in [0,1)$, $f(x) = \log_2(x+1)$. Consider the following propositions:  
1. $f(2014) + f(-2015) = 0$;  
2. The function $f(x)$ has a period of 2 on 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 $(-1,1)$.

Which of the above propositions are correct?

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