
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
(1) Given the inequality in terms of $x$, $3x - |-2x + 1| \geq a$, whose solution set is $[2, +\infty)$, find the value of the real number $a$;  
(2) If for $\forall x \in [1, 2]$, $x - |x - a| \leq 1$ always holds, find the range of values for the real number $a$.

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