
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
Let \(p, q\ be the roots of the quadratic equation \(x^{2}-3x-2=0\) and \(a=p^{3}+q^{3}\). Find \(a\).

If \(AH=a\), \(CK=36\), \(BK=12\) and \(BH=b\), find \(b\).

Let \(\sqrt{2x+23}+\sqrt{2x-1}=c\) and \(d=\sqrt{2x+23}-\sqrt{2x-1}\). Find \(d\).

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