
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 are considering a new design for their license plates with a sequence of four letters followed by four digits. The new pattern is designed to have each four-letter four-digit arrangement as a palindrome (reading the same left-to-right as right-to-left). Given that each arrangement is equally likely, find the probability that such a license plate will contain a palindrome in both the letter and digit sequences. Express your answer as a 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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