
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
Six students $A$, $B$, $C$, $D$, $E$, $F$ are standing in a row for a photo. If:<br/>
$(1)$ $A$ and $B$ are not standing together, how many ways can they be arranged?<br/>
$(2)$ $C$ and $D$ must stand together, how many ways can they be arranged?<br/>
$(3)$ $E$ is not at the beginning and $F$ is not at the end, how many ways can they be arranged?

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