
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
(I) Given the function $f\left( x \right)=\left| x-\dfrac{5}{2} \right|+\left| x-a \right|$, $x\in \mathbb{R}$, if the inequality $f\left( x \right)\geqslant a$ holds true for all $x\in \mathbb{R}$, find the maximum value of the real number $a$.

(II) Given positive numbers $x$, $y$, and $z$ that satisfy $x+2y+3z=1$, find the minimum value of $\dfrac{3}{x}+\dfrac{2}{y}+\dfrac{1}{z}$.

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