
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
Given two distinct numbers  $ b_1$  and  $ b_2$ , their product can be formed in two ways:  $ b_1 \times b_2$  and  $ b_2 \times b_1.$  Given three distinct numbers,  $ b_1, b_2, b_3,$  their product can be formed in twelve ways: 

 $ b_1\times(b_2 \times b_3);$   $ (b_1 \times b_2) \times b_3;$   $ b_1 \times (b_3 \times b_2);$   $ (b_1 \times b_3) \times b_2;$    $ b_2 \times (b_1 \times b_3);$   $ (b_2 \times b_1) \times b_3;$   $ b_2 \times(b_3 \times b_1);$   $ (b_2 \times b_3)\times b_1;$   $ b_3 \times(b_1 \times b_2);$   $ (b_3 \times b_1)\times b_2;$   $ b_3 \times(b_2 \times b_1);$   $ (b_3 \times b_2) \times b_1.$  

In how many ways can the product of  $ n$  distinct letters be formed?

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