
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 finite sequence {a_n} (n=1, 2, 3, ..., 6) such that a_n ∈ {1, 2, 3, ..., 10}, and for i ≠ j (i, j = 1, 2, 3, ..., 6), we have a_i ≠ a_j. If a_1 > a_2 > a_3 and a_4 < a_5 < a_6, determine the number of possible sequences {a_n} that satisfy these conditions.

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