
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 $f(x)$ is symmetric to the graph of $g(x) = 2^x$ with respect to the line $y=x$, and let $h(x) = f(1-|x|)$, then concerning the function $h(x)$, the following statements are made:  
① The graph of $h(x)$ is symmetric about the origin;    ② The graph of $h(x)$ is symmetric about the y-axis;  
③ The maximum value of $h(x)$ is 0;          ④ $h(x)$ is monotonically increasing in the interval $(-1, 1)$.  
Among these, the correct statement numbers are (write down all the correct statement numbers).

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