
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
How many nondecreasing sequences \(a_{1}, a_{2}, \ldots, a_{10}\) are composed entirely of at most three distinct numbers from the set \(\{1,2, \ldots, 9\}\)? For example, the sequences \(1,1,1,2,2,2,3,3,3,3\) and \(2,2,2,2,5,5,5,5,5,5\) are both allowed.

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