
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 $f(x)=|x-a|-2|x-1|$.
- (I) When $a=3$, solve the inequality $f(x) \geqslant 1$;
- (II) If $f(x)-|2x-5| \leqslant 0$ holds for any $x \in [1,2]$, find the range of the real number $a$.

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