
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
Many states have started using a sequence of three letters followed by a sequence of four digits as their standard license-plate pattern. Calculate the probability that such a license plate will contain at least one palindrome (either the three-letter arrangement reads the same left-to-right and right-to-left, or the four-digit arrangement reads the same left-to-right and right-to-left). Express your answer as a fraction $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, and find $m+n$.

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