
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
There are 8 identical balls, each labeled with a number from 1 to 8. Let event A be "selecting a ball with an odd number" and event B be "selecting a ball with a number that is a multiple of 3." <br/> $(1)$ Determine whether events A and B are independent, and explain the reason; <br/> $(2)$ Find $P(A+B)$.

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