
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 base of the pyramid is a square \(ABCD\) with a side length of 1.5, and the lateral edge \(SC\) is perpendicular to the plane of the base and has a length of 1.75. Points \(S\), \(B\), and \(D\) lie on the lateral surface of a cone whose vertex is at point \(A\), and point \(C\) is in the plane of the base of this cone. Find the surface area of the lateral surface of the cone.

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