
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 sum of two numbers is 40, and their product is 20. If the sum of their reciprocals is \(a\), find \(a\).

If \(b \mathrm{~cm}^{2}\) is the total surface area of a cube of side \((a+1) \mathrm{cm}\), find \(b\). 

One ball is taken at random from a bag containing \(b-4\) white balls and \(b+46\) red balls.

The length of a side of an equilateral triangle is \(c \mathrm{~cm}\). If its area is \(d \sqrt{3} \mathrm{~cm}^{2}\), find \(d\).

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