
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 updated their license plate format to include a sequence of four letters followed by a sequence of four digits. Given each four-letter and four-digit arrangement are equally likely, calculate the probability that such a license plate will contain at least one palindrome (a four-letter arrangement or a four-digit arrangement reading the same left-to-right and right-to-left). Express the result as a simplified fraction $\dfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers, and find $p+q$.

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