
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
(1) Let the function $f(x)=|x+2|+|x-a|$. If the inequality $f(x) \geqslant 3$ always holds for $x$ in $\mathbb{R}$, find the range of the real number $a$.

(2) Given positive numbers $x$, $y$, $z$ satisfying $x+2y+3z=1$, find the minimum value of $\frac{3}{x}+\frac{2}{y}+\frac{1}{z}$.

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