
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
Two types of steel plates need to be cut into three sizes $A$, $B$, and $C$. The number of each size that can be obtained from each type of steel plate is shown in the table:

\begin{tabular}{|l|c|c|c|}
\hline & Size $A$ & Size $B$ & Size $C$ \\
\hline First type of steel plate & 2 & 1 & 1 \\
\hline Second type of steel plate & 1 & 2 & 3 \\
\hline
\end{tabular}

If we need 15 pieces of size $A$, 18 pieces of size $B$, and 27 pieces of size $C$, find the minimum number of plates $m$ and $n$ of the two types required, so that $m + n$ is minimized.

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