
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
(12 points) Let the function $f(x) = |x - 1| + |x - a|$ where $a \in \mathbb{R}$.
(1) When $a = 4$, find the solution set of the inequality $f(x) \geq 5$;
(2) If $f(x) \geq 4$ holds for all $x \in \mathbb{R}$, find the range of the real number $a$.

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