
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
If the sum of roots of \(5 x^{2} + a x - 2 = 0\) is twice the product of roots, find the value of \(a\).

Given that \(y = a x^{2} - b x - 13\) passes through \((3,8)\), find the value of \(b\).

If there are \(c\) ways of arranging \(b\) girls in a circle, find the value of \(c\).

If \(\frac{c}{4}\) straight lines and 3 circles are drawn on a paper, and \(d\) is the largest number of points of intersection, find the value of \(d\).

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