
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 inequality concerning $x$: $|ax-1| + |ax-a| \geq 2$ ($a>0$).
(1) Find the solution set of the inequality when $a=1$.
(2) If the solution set of the inequality is the set of all real numbers $\mathbb{R}$, find the range of the real number $a$.

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