
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
Let the function $f(x) = |x - 1| + a|x - 2|$, where $a \in \mathbb{R}$.

(I) If the function $f(x)$ has a minimum value, find the range of values for $a$.

(II) If for any $x \in \mathbb{R}$, $f(x) \geq \frac{1}{2}$, find the value of $a$.

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