
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) A sphere centered at \(O\) touches the lateral edges \(SA, SB, SC\) of the pyramid \(SABC\) at points \(K, L, M\) respectively, and also touches its base \(ABC\). A plane, which is tangent to the sphere at the point closest to \(S\), is drawn. The area of the section of the pyramid \(SABC\) by this plane is \(5\), and \(\angle KSO = \arccos \frac{\sqrt{21}}{5}\). Find the area of triangle \(KLM\).

b) Additionally, suppose that \(SO = 36\) and the planes \(KLM\) and \(ABC\) are parallel. Find the volume of the pyramid \(2ABC\).

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