
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 the function $f(x)=e^{-|x|}+\cos \pi x$, consider the following statements:  
(1) The maximum value of $f(x)$ is $2$;  
(2) The sum of the zeros of $f(x)$ in $(-10,10)$ is $0$;  
(3) Any local maximum of $f(x)$ is greater than $1$.  
Among these, the correct statement(s) is/are __________.

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