
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 $f(x)=x^{2}-2x+k$, and $\log _{2}f(a)=2$, $f(\log _{2}a)=k$, $a > 0$, and $a\neq 1$.

1. Find the values of $a$ and $k$.
2. For what value of $x$ does $f(\log _{a}x)$ have a minimum value? Find this minimum value.

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