
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 $f(x)= \sqrt{x}+a|x+1|$, where $a$ is a real number,  
(1) If the function $f(x)$ has a zero, find the range of values for $a$;  
(2) When $a=-1$, find the range of values for the function $f(x)$.

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