
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 $$f(x)=\log_{a}{(3-ax)}$$  
(1) If the graph of $f(x)$ passes through the point $(4,1)$, find the value of $a$.  
(2) Does there exist a real number $a$ such that the function $f(x)$ is decreasing on the interval $[1,2]$ and its maximum value is 1? If it exists, find the value of $a$; if not, explain why.

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