
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
During the Lantern Festival, an interesting game called "Guess the Lantern Riddles" was organized. It is known that in an opaque box, there are several small lanterns with the same size and shape, labeled as $1$, $2$, and $3$, respectively. Each lantern has a riddle on it. There is $1$ lantern labeled as $1$, $2$ lanterns labeled as $2$, and $n$ lanterns labeled as $3$. If a contestant randomly picks one lantern from the box to solve the riddle, the probability of picking a lantern labeled as $3$ is $\frac{1}{4}$.  
(Ⅰ) Find the value of $n$;  
(Ⅱ) Without replacement, pick $2$ lanterns from the box. Let the label of the first picked lantern be $a$, and the label of the second picked lantern be $b$. Let event $A$ be "$a+b \geqslant 4$". Find the probability of event $A$.

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