
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
Let $a \gt 0$, and the function $f(x)=\sqrt{|x-a|}+\sqrt{|x+a|}$. If $g\left(x\right)=f\left(x\right)-b$ has exactly three distinct zeros, and $b$ is one of the zeros, then the real number $b$ is ______.

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