
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
Seven students, including students A, B, and C, stand in a row. Find the number of different ways to arrange them that satisfy the following conditions. (Provide answers in numbers)<br/>
$(1)$ A stands in the middle;<br/>
$(2)$ A is to the left of B (but not necessarily adjacent);<br/>
$(3)$ A, B, and C are not adjacent to each other.

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