
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 $f(x)=|x|$;
(I) If $2f(x-1)+f(2x-a)\geqslant 1$ holds for $\forall x\in\mathbb{R}$, find the range of values for the positive real number $a$;
(II) For the function $g(x)=3f(x)-f(x-t)$ $(t\neq 0)$, if the area enclosed by the graph of $g(x)$ and the $x$-axis is equal to $3$, find the value of the real number $t$.

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