
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
(The full score of this question is 12 points) Given the function $f(x) = |x - 1| + |x - 2|$. If the inequality $|a + b| + |a - b| \geq |a|f(x)$ (where $a \neq 0$, and $a, b \in \mathbb{R}$) always holds, find the range of values for the real number $x$.

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