
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 ordered sets $\left(a_{1}, a_{2}, \ldots, a_{n}\right)$ of $n$ natural numbers that satisfy the following conditions:

$$
1 \leq a_{1} \leq a_{2} \leq \ldots \leq a_{n} \quad \text{and} \quad a_{i} \leq i \quad (i = 1, 2, \ldots, n)
$$

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