
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 several dancers performing on stage, facing the audience to make formation changes. The rule of changes is as follows:  
When one dancer A<sub>1</sub> performs, the number of formation changes facing the audience is 1 for A<sub>1</sub>.  
When two dancers A<sub>1</sub> and A<sub>2</sub> perform, the number of formation changes facing the audience is 2, namely A<sub>1</sub>A<sub>2</sub> and A<sub>2</sub>A<sub>1</sub>, which is 1×2 kinds.  
When three dancers A<sub>1</sub>, A<sub>2</sub>, and A<sub>3</sub> perform, the number of formation changes facing the audience is 6, namely A<sub>1</sub>A<sub>2</sub>A<sub>3</sub>, A<sub>1</sub>A<sub>3</sub>A<sub>2</sub>, A<sub>2</sub>A<sub>1</sub>A<sub>3</sub>, A<sub>2</sub>A<sub>3</sub>A<sub>1</sub>, A<sub>3</sub>A<sub>1</sub>A<sub>2</sub>, and A<sub>3</sub>A<sub>2</sub>A<sub>1</sub>, which is 1×2×3 kinds.  
Please guess:  
(1) The number of formation changes facing the audience when four dancers A<sub>1</sub>, A<sub>2</sub>, A<sub>3</sub>, and A<sub>4</sub> perform is     kinds.  
(2) The number of formation changes facing the audience when six dancers A<sub>1</sub>, A<sub>2</sub>, A<sub>3</sub>, A<sub>4</sub>, A<sub>5</sub>, and A<sub>6</sub> perform is     kinds (expressed in scientific notation).  
(3) Using the digits 1, 2, 3, 4, 5, 6, 7 to form a 7-digit telephone number. If each digit can only be used once within the same telephone number, then the possible number of telephone numbers that can be formed is     .

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