
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 $f\left(x\right)=x^{2}-8x+10$, $x\in R$, the sequence $\{a_{n}\}$ is an arithmetic sequence with a common difference of $1$. If the value of $f(a_{1})+f(a_{2})+f(a_{3})$ is minimized, then $a_{1}=\_\_\_\_\_\_$.

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