
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
A 10-digit arrangement  $ 0,1,2,3,4,5,6,7,8,9$  is called *beautiful* if (i) when read left to right,  $ 0,1,2,3,4$  form an increasing sequence, and  $ 5,6,7,8,9$  form a decreasing sequence, and (ii)  $ 0$  is not the leftmost digit. For example,  $ 9807123654$  is a beautiful arrangement. Determine the number of beautiful arrangements.

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