
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
There are 8 different building blocks. Each block is either square or circular in shape, red or yellow in color, and printed with the city name Nanchang or Beijing. Suppose you sequentially select $n$ blocks $(2 \leqslant n \leqslant 8)$ from the 8 different blocks. Let $D_{n}$ represent the number of ways to select the blocks such that the block chosen at each subsequent step shares exactly two out of shape, color, and city name with the previously selected block. Determine $\max_{2 \leqslant n \leqslant 8} D_{n}$.

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