
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
Between what limits does the value of the following expression change, if \(a_{1}, a_{2}, \ldots, a_{10}\) are substituted in every possible order by the first 10 positive integers?

\[ 
K=\left|a_{1}-a_{2}\right|+\left|a_{2}-a_{3}\right|+\ldots+\left|a_{9}-a_{10}\right|+\left|a_{10}-a_{1}\right| 
\]

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