
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

Given that \( n \) and \( k \) are natural numbers and \( 1 < k < n \). If \(\frac{(1+2+3+\cdots+n)-k}{n-1}=10\) and \( n+k=a \), find the value of \( a \).

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