
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
Optional 4-5: Inequality Lecture
Given $f(x)=|x|+2|x-a| (a > 0)$.
(I) Solve the inequality $f(x)\leqslant 4$ when $a=1$;
(II) Find the range of real number $a$ if $f(x)\geqslant 4$ always holds.

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