
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
On a long strip of paper, the numbers $1, 2, 3, \ldots, n$ are written sequentially. The long strip is cut into five segments, each containing some consecutive natural numbers (the digits of a single number are not split across different segments). The average values of these five segments are given as $1234, 345, 128, 19,$ and $9.5$ (the order of these numbers is shuffled). What is the value of $\mathbf{n}$?

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