
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
A certain state decides to use a sequence of four letters followed by four digits as a new license-plate pattern. Each four-letter four-digit arrangement is equally likely. Calculate the probability that such a license plate will contain at least one palindrome (either a four-letter arrangement or a four-digit arrangement that reads the same left-to-right and right-to-left). Express this probability in the form $\dfrac{m}{n}$, 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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