
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
Given that a customer draws two cards from six marked with black 1, black 2, black 3, black 4, red 1, and red 3, determine the respective probabilities for the Flush, Same color, Straight, Pair, and Others categories.

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