
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 $f(x) = |x-a| - |2x-1|$.  
(1) When $a=2$, find the solution set for $f(x) + 3 \geq 0$;  
(2) When $x \in [1, 3]$, $f(x) \leq 3$ always holds, find the range of values for $a$.

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