
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 $a_{i}\in N*\left(i=1,2,\ldots ,9\right)$ and $a_{k}=a_{k-1}+1$ or $a_{k}=a_{k+1}-1\left(2\leqslant k\leqslant 8\right)$ holds for only one $a_{i}$, where $a_{1}=6$ and $a_{9}=9$. Find the minimum value of $a_{1}+\ldots +a_{9}$.

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