
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
Let \( n \) be a positive integer. Find the number of permutations \( a_{1}, a_{2}, \ldots, a_{n} \) of the sequence \( 1, 2, \ldots, n \) satisfying
\[ a_{1} \leq 2 a_{2} \leq 3 a_{3} \leq \ldots \leq n a_{n} . \]

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