
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 quadrilateral pyramid \( S A B C D \) is a quadrilateral \( A B C D \) with \( A B = A D = 6 \), \( C B = C D = 2 \), and the sides \( A B \) and \( B C \) are perpendicular to each other. All the lateral faces are inclined to the plane of the base at an angle of \( 60^{\circ} \). Find the volume \( V \) of the pyramid, given that \( V > 12 \).

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