
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
Arrange the $5$ different products $A$, $B$, $C$, $D$, $E$ in a row.<br/>$(1)$ How many different ways are there to arrange the products $A$ and $B$ next to each other?<br/>$(2)$ If the products $A$ and $B$ are next to each other, and the products $A$ and $C$ are not next to each other, how many different ways are there to arrange them?

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