
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 points \(A(4,5)\), \(B(4,0)\) and \(C(0,5)\), compute the line integral of the second kind \(\int_{L}(4 x+8 y+5) d x+(9 x+8) d y\) where \(L:\)
a) the line segment \(OA\);
b) the broken line \(OCA\);
c) the parabola \(y=k x^{2}\) passing through the points \(O\) and \(A\).

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