
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
How many different arrangements are there for 4 men and 3 women to stand in a row, if the following conditions are met?
(1) No two women may stand next to each other. How many arrangements are there?
(2) Man A cannot stand in the first position, and Man B cannot stand in the last position. How many arrangements are there?
(3) Men A, B, and C must stand in a fixed sequence. How many arrangements are there?
(4) Man A must stand to the left of Man B (not necessarily adjacent). How many different arrangements are there?

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