
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 update their license plate design to a sequence of four letters followed by four digits. The license plates are generated such that each four-letter four-digit arrangement is equally likely. Calculate the probability that such a license plate will contain at least one two-letter palindrome either in the four-letter arrangement or in the four-digit arrangement. A two-letter palindrome reads the same forward and backward. Express the probability as $\dfrac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q.$

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