
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 $(b_1, b_2, b_3, \dots, b_{15})$ be a permutation of $(1, 2, 3, \dots, 15)$ for which
$b_1 > b_2 > b_3 > b_4 > b_5 > b_6 > b_7 \mathrm{\ and \ } b_7 < b_8 < b_9 < b_{10} < b_{11} < b_{12} < b_{13} < b_{14} < b_{15}$.
Find the number of such permutations.

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