
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
Elective 4-5: Selected Topics on Inequalities  
Given the function $f(x) = |x + a| + |x - 2|$,  
(1) When $a = -3$, find the solution set of the inequality $f(x) \geq 3$;  
(2) If the solution set of $f(x) \leq |x - 4|$ contains $[1, 2]$, find the range of values for $a$.

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