
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 $(a_1,a_2,a_3,\ldots,a_{18})$ be a permutation of $(1,2,3,\ldots,18)$ for which
$a_1>a_2>\cdots>a_9$ and $a_9<a_{10}<\cdots<a_{18}.$
Determine how many such permutations exist.

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