
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
According to the environmental protection department, the pollution index at a certain location is directly proportional to the intensity of nearby pollution sources and inversely proportional to the square of the distance from the pollution source, with a proportionality constant of $k$ ($k>0$). It is known that two chemical plants (pollution sources), A and B, which are 18km apart, have pollution intensities of $a$ and $b$, respectively. The pollution index $y$ at any point C on the line connecting the two chemical plants is equal to the sum of the pollution indices from both chemical plants. Let AC = $x$ (km).

(1) Express $y$ as a function of $x$;  
(2) If $a=1$, and $y$ reaches its minimum value when $x=6$, find the value of $b$.

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