
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 function $f(x)=|2x-a|-|x+3|$, where $a \in \mathbb{R}$.
(I) When $a=1$, find the minimum value of $f(x)$;
(II) When $x \in [0,3]$, find the range of $a$ such that $f(x) \leqslant 4$ always holds.

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