
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
There are two models of LCD television on sale. One is a '20 inch' standard model while the other is a '20 inch' widescreen model. The ratio of the length to the height of the standard model is \(4: 3\), while that of the widescreen model is \(16: 9\). Television screens are measured by the length of their diagonals, so both models have the same diagonal length of 20 inches. If the ratio of the area of the standard model to that of the widescreen model is \(A: 300\), find the value of \(A\).

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