
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
(The full score of this question is 12 points)  
Given $f(x) = x^2 - x + k$, and $\log_2{f(a)} = 2$, $f(\log_2{a}) = k$ ($a > 0$, $a \neq 1$).  
(I) Find the values of $a$ and $k$;  
(II) For what value of $x$ does $f(\log_a{x})$ have the minimum value? And find this minimum value.

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