
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
Let $(b_1, b_2, b_3, \ldots, b_{20})$ be a permutation of $(1, 2, 3, \ldots, 20)$ for which $b_1 > b_2 > b_3 > b_4 > b_5 > b_6 > b_7 > b_8 > b_9 \mathrm{\ and \ } b_9 < b_{10} < b_{11} < b_{12} < b_{13} < b_{14} < b_{15} < b_{16} < b_{17} < b_{18} < b_{19} < b_{20}.$
An example of such a permutation is $(9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20)$. Find the number of such permutations.

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