
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
On the edge $SA$ of a regular quadrilateral pyramid $SABCD$ with vertex $S$, a point $K$ is marked such that $AK:KS=2:3$. Point $K$ is the vertex of a right circular cone, on the circumference of the base of which lie three vertices of the pyramid $SABCD$.

a) Find the ratio $CS: CD$.

b) Let it additionally be known that the height of the pyramid $SABCD$ is 5. Find the volume of the cone.

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