
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
In a new vehicle registration system, license plates consist of a sequence of four letters followed by a sequence of four digits. Calculate the probability that a randomly chosen license plate contains at least one palindrome (either the four-letter arrangement or the four-digit arrangement reads the same left-to-right as right-to-left), which cannot start with zeros or 'A' letter. Express your answer as a reduced fraction.

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