
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 $f(x)=(\frac{1}{2})^{x}$ is symmetric to the graph of the function $y=g(x)$ about the line $y=x$, and let $h(x)=g(2-|x|)$, then regarding $h(x)$, the following statements are made:  
1. $h(x)$ is an even function;  
2. The graph of $h(x)$ is symmetric about the origin;  
3. The minimum value of $h(x)$ is $-1$.  
Among these statements, the correct statement number(s) is/are __________ (Fill in the correct statement number(s)).

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