
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
Fengfeng, Leilei, and Feifei have different eating habits. The table below shows today's lunch menu at the school cafeteria. In the table, "√" indicates that they like the food, and "×" indicates that they refuse the food. If each person must order one dish they like for lunch, and no two people can order the same dish, how many different ordering schemes are possible?

\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline & Papaya Chicken & Spiced Beef & Braised Lamb & Grilled Prawns & & Fresh Sprouts & Garlic Cabbage & Braised Eggplant \\
\hline Fengfeng & $\times$ & $\times$ & $\times$ & $\times$ & $\times$ & √ & √ & √ \\
\hline Leilei & √ & √ & √ & $\times$ & $\times$ & √ & √ & $\times$ \\
\hline FeiFei & √ & $\times$ & $\times$ & √ & √ & √ & $\times$ & √ \\
\hline
\end{tabular}

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