
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 with center \( O \) is tangent to the lateral edges \( SA, SB, SC \) of a pyramid \( SABC \) at points \( K, L, M \) respectively, and also to its base \( ABC \). A plane tangent to the sphere passes through the point of the sphere closest to point \( S \). The area of the section of pyramid \( SABC \) by this plane equals 9, and \( \angle KSO = \arccos \frac{\sqrt{35}}{6} \). Find the area of triangle \( KLM \).

b) Additionally, let it be known that \( SO = 25 \), and planes \( KLM \) and \( ABC \) are parallel. Find the volume of pyramid \( 2ABC \).

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