
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
Given a regular triangular pyramid $SABC$ (where $S$ is its apex). The edge $SC$ of this pyramid coincides with a lateral edge of a regular triangular prism $A_1 B_1 C A_2 B_2 S$ ($A_1A_2$, $B_1B_2$, and $CS$ are lateral edges, and $A_1B_1C$ is one of the bases). The vertices $A_1$ and $B_1$ lie in the plane of the face $SAB$ of the pyramid. What fraction of the pyramid's volume is occupied by the part of the pyramid that lies within the prism, given that the ratio of the length of the pyramid's lateral edge to the side of its base is $2 / \sqrt{3}$?

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