
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 $4$ male athletes and $3$ female athletes.<br/>$(1)$ Now $7$ athletes are lined up. If all female athletes are together, how many ways are there to arrange them?<br/>$(2)$ Now the male athletes are sent to two different venues for training, with at least one athlete in each venue. Each athlete goes to one venue. How many different ways are there to allocate them?

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