
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
Given a sequence $\{a_n\}$ ($n=1,2,3,\ldots,6$) satisfying $a_n \in \{1,2,3,4,5,6,7\}$, and for $i \neq j$ ($i,j=1,2,3,\ldots,6$), $a_i \neq a_j$. If $a_1 > a_2 > a_3$ and $a_4 < a_5 < a_6$, find the number of sequences $\{a_n\}$ that meet the conditions.

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