
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 $f(x)=|x-a|$, where $a\in\mathbb{R}$.
(I) Find the range of $a$ such that when $-1\leqslant x\leqslant 3$, $f(x)\leqslant 3$.
(II) If for any $x\in\mathbb{R}$, $f(x-a)+f(x+a)\geqslant 1-2a$ always holds, find the minimum value of the real number $a$.

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