
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 $f(x)=4-|x|-|x-3|$

(Ⅰ) Solve the inequality $f(x+ \dfrac{3}{2} )\geqslant 0$ for its solution set;

(Ⅱ) If $p$, $q$, $r$ are positive real numbers, and $ \dfrac{1}{3p}+ \dfrac{1}{2q}+ \dfrac{1}{r}=4 $, find the minimum value of $3p+2q+r$.

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