
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
The cards of a standard 52-card deck are dealt out in a circle. What is the expected number of sequences of three adjacent cards where the first two cards are both black, and the third card is red?

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