
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
The integers  $1, 2, \dots, n$  are written in order on a long slip of paper. The slip is then cut into five pieces, so that each piece consists of some (nonempty) consecutive set of integers.  The averages of the numbers on the five slips are  $1234$ ,  $345$ ,  $128$ ,  $19$ , and  $9.5$  in some order.  Compute  $n$ .

*Proposed by Evan Chen*

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