
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  $a_1$ ,  $a_2$ ,  $\dots a_n$  of the
sequence  $1$ ,  $2$ ,  $\dots$  ,  $n$  satisfying  $$ a_1 \le 2a_2\le 3a_3 \le \dots \le na_n $$  .

Proposed by United Kingdom

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