
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 $(a_1,a_2,a_3,\ldots,a_{14})$ be a permutation of $(1,2,3,\ldots,14)$ for which
$a_1>a_2>a_3>a_4>a_5>a_6 \mathrm{\ and \ } a_7<a_8<a_9<a_{10}<a_{11}<a_{12}<a_{13}<a_{14}.$
Find the number of such permutations.

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