
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
For the function $f(x)=e^{\sin x}+e^{\cos x}$, which of the following statements are correct?  
① The smallest positive period of $f(x)$ is $\pi$;  
② $y=f(x+\frac{π}{4})$ is an even function;  
③ The equation $f(x)=4$ has exactly three solutions in the interval $[0,\pi]$;  
④ The minimum value of $f(x)$ is $2e^{-\frac{\sqrt{2}}{2}}$.

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