
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
Suppose $1 \leq r \leq n$. For an ordered tuple $\left(x_{1}, x_{2}, \cdots, x_{r}\right)$ where each $x_{j} \in\{1,2, \cdots, n\}$, there are at most $i-1$ elements less than or equal to $i$ for each $i=1$, $2, \cdots, n$. Find the number of such $r$-tuples.

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