
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
A quadrilateral contains an inscribed circle (i.e., a circle tangent to the four sides of the quadrilateral). The ratio of the perimeter of the quadrilateral to that of the circle is \(4:3\). The ratio of the area of the quadrilateral to that of the circle, expressed in its lowest terms, is \(a:b\). What is the value of \(100a + 49b\)?

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