
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. There are  $N$  tasks, numbered  $1, 2, 3, \ldots, N$ , to be completed. Each task takes one minute to complete and the tasks must be completed subjected to the following conditions:


- Any number of tasks can be performed at the same time.
- For any positive integer  $k$ , task  $k$  begins immediately after all tasks whose numbers are divisors of  $k$ , not including  $k$  itself, are completed.
- Task 1 is the first task to begin, and it begins by itself.

Suppose  $N = 2017$ . How many minutes does it take for all of the tasks to complete? Which tasks are the last ones to complete?

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