
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
In a bag, there are $4$ balls of the same size and material, labeled $1$, $2$, $3$, $4$. Two balls are randomly drawn from the bag without replacement. Let event $A$ be drawing the ball labeled $2$ on the first draw, and event $B$ be the sum of the numbers on the two balls drawn is $5$.  
$(1)$ Write down the sample space of this experiment.  
$(2)$ Determine whether events $A$ and $B$ are independent, and explain the reason.  
$(3)$ What is the most likely sum of the two numbers drawn? Explain the reason.

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