
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
Let the function $f(x)$ be defined on $\mathbb{R}$. Among the following functions: 
1. $y = -|f(x)|$
2. $y = |x| \cdot f(x^2)$
3. $y = -f(-x)$
4. $y = f(x) + f(-x)$

Identify the even functions. (Write down all correct serial numbers.)

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