
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
Arrange six positive integers \(a, b, c, d, e, f\) in a sequence in alphabetical order such that \(a=1\). If any positive integer is greater than 1, then the number that is one less than this integer must appear to its left. For example, \(1,1,2,1,3,2\) meets the requirement; \(1,2,3,1,4,1\) meets the requirement; \(1,2,2,4,3,2\) does not meet the requirement. Find the number of different sequences that meet the requirement.

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