
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 real numbers $a>0$, $b>0$, the maximum value of the function $f(x) = |x-a| - |x+b|$ is 3.  
(I) Find the value of $a+b$;  
(II) Let the function $g(x) = -x^2 - ax - b$, if for all $x \geq a$, $g(x) < f(x)$, find the range of values for $a$.

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