
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 of the pyramid \( T A B C D \) is the trapezoid \( A B C D \) where \( B C \parallel A D \). The distances from points \( A \) and \( B \) to the plane \( T C D \) are \( r_1 \) and \( r_2 \) respectively. The area of triangle \( T C D \) is \( S \). Find the volume of the pyramid \( T A B C D \).

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