
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 graph of the function $f(x) = x$ is symmetric to the graph of the function $g(x)$ with respect to the line $y = x$, and let $h(x) = g(1 - |x|)$, then concerning the function $h(x)$, the following statements are made:
1. The graph of $h(x)$ is symmetric about the origin.
2. $h(x)$ is an even function.
3. The minimum value of $h(x)$ is 0.
4. $h(x)$ is a decreasing function on the interval $(0,1)$.

Among these statements, the correct ones are \_\_\_\_\_\_\_\_ (Note: Fill in the sequence numbers of all correct statements).

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