
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 $f(x + \frac{3}{2}) \geq 0$ for its solution set;  
(Ⅱ) If $p$, $q$, and $r$ are positive real numbers, and $\frac{1}{3p} + \frac{1}{2q} + \frac{1}{r} = 4$, find the minimum value of $3p + 2q + r$.

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