
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
In a crossword puzzle, three-digit powers of $2$ and $3$ are used. We need to find the only possible digit for the outlined square where these two numbers intersect; specifically, for "across" the number is a power of $2$, and for "down" it is a power of $3".
\[\begin{array}{lcl} \textbf{ACROSS} & & \textbf{DOWN} \\ \textbf{2}.~ 2^m & & \textbf{1}.~ 3^n \end{array}\]
A) 0  
B) 1  
C) 2  
D) 5  
E) 6

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