
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 the function $f(x)=\left\{\begin{array}{l}{x^2}-2ax+8, x\leq 1\\ x+\frac{4}{x}+2a, x>1\end{array}\right.$, if the minimum value of $f(x)$ is $f(1)$, find the value of the real number $a$.

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