
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 base side of the regular quadrilateral pyramid \( S A B C D \) (\( S \) is the apex) is equal to 10. Points \( E \) and \( F \) are located on edges \( D C \) and \( B C \) respectively, with \( C E = 6 \) and \( C F = 9 \). It is known that for this pyramid there exists a unique cone whose vertex coincides with point \( E \), the center of the base lies on the line \( S A \), and the segment \( E F \) is one of the generatrices. Find the volume of this cone.

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