
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 the function $g(x) = 2^x$ with respect to the line $y=x$, and let $h(x) = f(1-|x|)$, then regarding the function $h(x)$, the following statements are made:  
(1) The graph of $h(x)$ is symmetric about the origin $(0,0)$.  
(2) The graph of $h(x)$ is symmetric about the y-axis.  
(3) The minimum value of $h(x)$ is 0.  
(4) $h(x)$ is monotonically increasing in the interval $(-1,0)$.  
The correct statements are \_\_\_\_\_\_.

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