
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
A regular quadrilateral frustum \( ABCD-A_{1}B_{1}C_{1}D_{1} \) has a height of \( 6 \) cm, and the side lengths of the upper and lower bases are \( 4 \) cm and \( 8 \) cm, respectively. A cross-section is made through one of the diagonals \( BD_{1} \) and is parallel to the diagonal \( AC \) of the base. Find the area of this cross-section.

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