
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
Amanda, Chloe, and Ethan are siblings. Their names consist of 6, 5, and 4 letters respectively, placed on identical cards so that each card contains one letter. Without replacement, two cards are selected at random from the 15 cards. What is the probability that one letter is from Amanda's name and the other from either Chloe's or Ethan's name? Express your answer as a common fraction.

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