
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
Find the number of 20-tuples of integers \(x_{1}, \ldots, x_{10}, y_{1}, \ldots, y_{10}\) with the following properties:
- \(1 \leq x_{i} \leq 10\) and \(1 \leq y_{i} \leq 10\) for each \(i\);
- \(x_{i} \leq x_{i+1}\) for \(i=1, \ldots, 9\);
- if \(x_{i}=x_{i+1}\), then \(y_{i} \leq y_{i+1}\).

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