
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 the decimal system, the place value for each digit corresponds to powers of 10. For instance, \( 24_{10} = 2 \times 10 + 4 \times 1 \) and \( 365_{10} = 3 \times 10^2 + 6 \times 10 + 5 \times 1 \). Computers use the binary system, where the place value corresponds to powers of 2. For example, \( 7_{10} = 1 \times 2^2 + 1 \times 2 + 1 \times 1 = 111_{2} \) and \( 12_{10} = 1 \times 2^3 + 1 \times 2^2 + 0 \times 2 + 0 \times 1 = 1100_{2} \).

If a natural number can be expressed in base \( m \) as \( 45_m \) and in base \( n \) as \( 54_n \), find the smallest values of \( m \) and \( n \).  
  
Minimum values of \( m = \) \_\_\_\_\_ , \( n = \) \_\_\_\_\_ .

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