
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
Fix positive integers  $n,j,k$ .How many integer sequences are there of the form  $1\le a_1<a_2<\ldots<a_k\le n$ ,where  $a_{i+1}-a_i\ge j$  for all  $1\le i\le k-1$ .

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